Graphics.Rendering.Chart.Axis.Types:linMap from Chart-1.5.3

Percentage Accurate: 67.7% → 91.6%

Time: 25.8s

Alternatives: 24

Speedup: 0.6×

Specification

Math

\[\begin{array}{l} \\ x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \end{array} \]

FPCore

(FPCore (x y z t a) :precision binary64 (+ x (/ (* (- y x) (- z t)) (- a t))))

C

double code(double x, double y, double z, double t, double a) {
	return x + (((y - x) * (z - t)) / (a - t));
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    code = x + (((y - x) * (z - t)) / (a - t))
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	return x + (((y - x) * (z - t)) / (a - t));
}

Python

def code(x, y, z, t, a):
	return x + (((y - x) * (z - t)) / (a - t))

Julia

function code(x, y, z, t, a)
	return Float64(x + Float64(Float64(Float64(y - x) * Float64(z - t)) / Float64(a - t)))
end

MATLAB

function tmp = code(x, y, z, t, a)
	tmp = x + (((y - x) * (z - t)) / (a - t));
end

Wolfram

code[x_, y_, z_, t_, a_] := N[(x + N[(N[(N[(y - x), $MachinePrecision] * N[(z - t), $MachinePrecision]), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Initial Program: 67.7% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \end{array} \]

FPCore

(FPCore (x y z t a) :precision binary64 (+ x (/ (* (- y x) (- z t)) (- a t))))

C

double code(double x, double y, double z, double t, double a) {
	return x + (((y - x) * (z - t)) / (a - t));
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    code = x + (((y - x) * (z - t)) / (a - t))
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	return x + (((y - x) * (z - t)) / (a - t));
}

Python

def code(x, y, z, t, a):
	return x + (((y - x) * (z - t)) / (a - t))

Julia

function code(x, y, z, t, a)
	return Float64(x + Float64(Float64(Float64(y - x) * Float64(z - t)) / Float64(a - t)))
end

MATLAB

function tmp = code(x, y, z, t, a)
	tmp = x + (((y - x) * (z - t)) / (a - t));
end

Wolfram

code[x_, y_, z_, t_, a_] := N[(x + N[(N[(N[(y - x), $MachinePrecision] * N[(z - t), $MachinePrecision]), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Alternative 1: 91.6% accurate, 0.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq 1.45 \cdot 10^{+181}:\\ \;\;\;\;\mathsf{fma}\left(-x, \frac{z}{a - t} + \left(-1 - \frac{t}{a - t}\right), \frac{y}{\frac{a - t}{z - t}}\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(z - a, \frac{x}{t}, y\right) + \frac{y}{t} \cdot \left(a - z\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= t 1.45e+181)
   (fma
    (- x)
    (+ (/ z (- a t)) (- -1.0 (/ t (- a t))))
    (/ y (/ (- a t) (- z t))))
   (+ (fma (- z a) (/ x t) y) (* (/ y t) (- a z)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= 1.45e+181) {
		tmp = fma(-x, ((z / (a - t)) + (-1.0 - (t / (a - t)))), (y / ((a - t) / (z - t))));
	} else {
		tmp = fma((z - a), (x / t), y) + ((y / t) * (a - z));
	}
	return tmp;
}

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (t <= 1.45e+181)
		tmp = fma(Float64(-x), Float64(Float64(z / Float64(a - t)) + Float64(-1.0 - Float64(t / Float64(a - t)))), Float64(y / Float64(Float64(a - t) / Float64(z - t))));
	else
		tmp = Float64(fma(Float64(z - a), Float64(x / t), y) + Float64(Float64(y / t) * Float64(a - z)));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[t, 1.45e+181], N[((-x) * N[(N[(z / N[(a - t), $MachinePrecision]), $MachinePrecision] + N[(-1.0 - N[(t / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(y / N[(N[(a - t), $MachinePrecision] / N[(z - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(N[(z - a), $MachinePrecision] * N[(x / t), $MachinePrecision] + y), $MachinePrecision] + N[(N[(y / t), $MachinePrecision] * N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < 1.45e181

   1. Initial program 71.7%

      \[x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \]
   2. Step-by-step derivation

      1. +-commutative 71.7%

         \[\leadsto \color{blue}{\frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} + x} \]

      2. associate-*l/ 80.2%

         \[\leadsto \color{blue}{\frac{y - x}{a - t} \cdot \left(z - t\right)} + x \]

      3. fma-def 80.3%

         \[\leadsto \color{blue}{\mathsf{fma}\left(\frac{y - x}{a - t}, z - t, x\right)} \]

   3. Simplified 80.3%

      \[\leadsto \color{blue}{\mathsf{fma}\left(\frac{y - x}{a - t}, z - t, x\right)} \]
   4. Add Preprocessing
   5. Step-by-step derivation

      1. fma-udef 80.2%

         \[\leadsto \color{blue}{\frac{y - x}{a - t} \cdot \left(z - t\right) + x} \]

      2. associate-/r/ 88.2%

         \[\leadsto \color{blue}{\frac{y - x}{\frac{a - t}{z - t}}} + x \]

      3. div-inv 88.1%

         \[\leadsto \color{blue}{\left(y - x\right) \cdot \frac{1}{\frac{a - t}{z - t}}} + x \]

      4. clear-num 88.2%

         \[\leadsto \left(y - x\right) \cdot \color{blue}{\frac{z - t}{a - t}} + x \]

   6. Applied egg-rr 88.2%

      \[\leadsto \color{blue}{\left(y - x\right) \cdot \frac{z - t}{a - t} + x} \]

   7. Taylor expanded in x around -inf 84.3%

      \[\leadsto \color{blue}{-1 \cdot \left(x \cdot \left(\frac{z}{a - t} - \left(1 + \frac{t}{a - t}\right)\right)\right) + \frac{y \cdot \left(z - t\right)}{a - t}} \]
   8. Step-by-step derivation

      1. neg-mul-1 84.3%

         \[\leadsto \color{blue}{\left(-x \cdot \left(\frac{z}{a - t} - \left(1 + \frac{t}{a - t}\right)\right)\right)} + \frac{y \cdot \left(z - t\right)}{a - t} \]

      2. distribute-lft-neg-in 84.3%

         \[\leadsto \color{blue}{\left(-x\right) \cdot \left(\frac{z}{a - t} - \left(1 + \frac{t}{a - t}\right)\right)} + \frac{y \cdot \left(z - t\right)}{a - t} \]

      3. fma-def 84.4%

         \[\leadsto \color{blue}{\mathsf{fma}\left(-x, \frac{z}{a - t} - \left(1 + \frac{t}{a - t}\right), \frac{y \cdot \left(z - t\right)}{a - t}\right)} \]

      4. +-commutative 84.4%

         \[\leadsto \mathsf{fma}\left(-x, \frac{z}{a - t} - \color{blue}{\left(\frac{t}{a - t} + 1\right)}, \frac{y \cdot \left(z - t\right)}{a - t}\right) \]

      5. associate-/l* 96.5%

         \[\leadsto \mathsf{fma}\left(-x, \frac{z}{a - t} - \left(\frac{t}{a - t} + 1\right), \color{blue}{\frac{y}{\frac{a - t}{z - t}}}\right) \]

   9. Simplified 96.5%

      \[\leadsto \color{blue}{\mathsf{fma}\left(-x, \frac{z}{a - t} - \left(\frac{t}{a - t} + 1\right), \frac{y}{\frac{a - t}{z - t}}\right)} \]

   if 1.45e181 < t

   1. Initial program 15.8%

      \[x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \]
   2. Step-by-step derivation

      1. associate-*l/ 34.7%

         \[\leadsto x + \color{blue}{\frac{y - x}{a - t} \cdot \left(z - t\right)} \]

   3. Simplified 34.7%

      \[\leadsto \color{blue}{x + \frac{y - x}{a - t} \cdot \left(z - t\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in t around inf 73.8%

      \[\leadsto \color{blue}{\left(y + -1 \cdot \frac{z \cdot \left(y - x\right)}{t}\right) - -1 \cdot \frac{a \cdot \left(y - x\right)}{t}} \]
   6. Step-by-step derivation

      1. associate--l+ 73.8%

         \[\leadsto \color{blue}{y + \left(-1 \cdot \frac{z \cdot \left(y - x\right)}{t} - -1 \cdot \frac{a \cdot \left(y - x\right)}{t}\right)} \]

      2. associate-*r/ 73.8%

         \[\leadsto y + \left(\color{blue}{\frac{-1 \cdot \left(z \cdot \left(y - x\right)\right)}{t}} - -1 \cdot \frac{a \cdot \left(y - x\right)}{t}\right) \]

      3. associate-*r/ 73.8%

         \[\leadsto y + \left(\frac{-1 \cdot \left(z \cdot \left(y - x\right)\right)}{t} - \color{blue}{\frac{-1 \cdot \left(a \cdot \left(y - x\right)\right)}{t}}\right) \]

      4. div-sub 73.8%

         \[\leadsto y + \color{blue}{\frac{-1 \cdot \left(z \cdot \left(y - x\right)\right) - -1 \cdot \left(a \cdot \left(y - x\right)\right)}{t}} \]

      5. distribute-lft-out-- 73.8%

         \[\leadsto y + \frac{\color{blue}{-1 \cdot \left(z \cdot \left(y - x\right) - a \cdot \left(y - x\right)\right)}}{t} \]

      6. associate-*r/ 73.8%

         \[\leadsto y + \color{blue}{-1 \cdot \frac{z \cdot \left(y - x\right) - a \cdot \left(y - x\right)}{t}} \]

      7. mul-1-neg 73.8%

         \[\leadsto y + \color{blue}{\left(-\frac{z \cdot \left(y - x\right) - a \cdot \left(y - x\right)}{t}\right)} \]

      8. unsub-neg 73.8%

         \[\leadsto \color{blue}{y - \frac{z \cdot \left(y - x\right) - a \cdot \left(y - x\right)}{t}} \]

      9. distribute-rgt-out-- 73.8%

         \[\leadsto y - \frac{\color{blue}{\left(y - x\right) \cdot \left(z - a\right)}}{t} \]

      10. associate-/l* 96.8%

          \[\leadsto y - \color{blue}{\frac{y - x}{\frac{t}{z - a}}} \]

   7. Simplified 96.8%

      \[\leadsto \color{blue}{y - \frac{y - x}{\frac{t}{z - a}}} \]

   8. Taylor expanded in x around 0 73.7%

      \[\leadsto \color{blue}{\left(y + \frac{x \cdot \left(z - a\right)}{t}\right) - \frac{y \cdot \left(z - a\right)}{t}} \]
   9. Step-by-step derivation

      1. +-commutative 73.7%

         \[\leadsto \color{blue}{\left(\frac{x \cdot \left(z - a\right)}{t} + y\right)} - \frac{y \cdot \left(z - a\right)}{t} \]

      2. *-commutative 73.7%

         \[\leadsto \left(\frac{\color{blue}{\left(z - a\right) \cdot x}}{t} + y\right) - \frac{y \cdot \left(z - a\right)}{t} \]

      3. associate-*r/ 88.0%

         \[\leadsto \left(\color{blue}{\left(z - a\right) \cdot \frac{x}{t}} + y\right) - \frac{y \cdot \left(z - a\right)}{t} \]

      4. fma-def 88.0%

         \[\leadsto \color{blue}{\mathsf{fma}\left(z - a, \frac{x}{t}, y\right)} - \frac{y \cdot \left(z - a\right)}{t} \]

      5. associate-/l* 96.9%

         \[\leadsto \mathsf{fma}\left(z - a, \frac{x}{t}, y\right) - \color{blue}{\frac{y}{\frac{t}{z - a}}} \]

      6. associate-/r/ 96.9%

         \[\leadsto \mathsf{fma}\left(z - a, \frac{x}{t}, y\right) - \color{blue}{\frac{y}{t} \cdot \left(z - a\right)} \]

   10. Simplified 96.9%

       \[\leadsto \color{blue}{\mathsf{fma}\left(z - a, \frac{x}{t}, y\right) - \frac{y}{t} \cdot \left(z - a\right)} \]
3. Recombined 2 regimes into one program.

4. Final simplification 96.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq 1.45 \cdot 10^{+181}:\\ \;\;\;\;\mathsf{fma}\left(-x, \frac{z}{a - t} + \left(-1 - \frac{t}{a - t}\right), \frac{y}{\frac{a - t}{z - t}}\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(z - a, \frac{x}{t}, y\right) + \frac{y}{t} \cdot \left(a - z\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 2: 89.3% accurate, 0.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -1.5 \cdot 10^{+167} \lor \neg \left(t \leq 5.8 \cdot 10^{+141}\right):\\ \;\;\;\;y + \frac{x - y}{\frac{t}{z - a}}\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(\frac{z - t}{a - t}, y - x, x\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= t -1.5e+167) (not (<= t 5.8e+141)))
   (+ y (/ (- x y) (/ t (- z a))))
   (fma (/ (- z t) (- a t)) (- y x) x)))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((t <= -1.5e+167) || !(t <= 5.8e+141)) {
		tmp = y + ((x - y) / (t / (z - a)));
	} else {
		tmp = fma(((z - t) / (a - t)), (y - x), x);
	}
	return tmp;
}

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((t <= -1.5e+167) || !(t <= 5.8e+141))
		tmp = Float64(y + Float64(Float64(x - y) / Float64(t / Float64(z - a))));
	else
		tmp = fma(Float64(Float64(z - t) / Float64(a - t)), Float64(y - x), x);
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[t, -1.5e+167], N[Not[LessEqual[t, 5.8e+141]], $MachinePrecision]], N[(y + N[(N[(x - y), $MachinePrecision] / N[(t / N[(z - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(N[(z - t), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision] * N[(y - x), $MachinePrecision] + x), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -1.50000000000000006e167 or 5.80000000000000013e141 < t

   1. Initial program 20.3%

      \[x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \]
   2. Step-by-step derivation

      1. associate-*l/ 49.6%

         \[\leadsto x + \color{blue}{\frac{y - x}{a - t} \cdot \left(z - t\right)} \]

   3. Simplified 49.6%

      \[\leadsto \color{blue}{x + \frac{y - x}{a - t} \cdot \left(z - t\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in t around inf 63.8%

      \[\leadsto \color{blue}{\left(y + -1 \cdot \frac{z \cdot \left(y - x\right)}{t}\right) - -1 \cdot \frac{a \cdot \left(y - x\right)}{t}} \]
   6. Step-by-step derivation

      1. associate--l+ 63.8%

         \[\leadsto \color{blue}{y + \left(-1 \cdot \frac{z \cdot \left(y - x\right)}{t} - -1 \cdot \frac{a \cdot \left(y - x\right)}{t}\right)} \]

      2. associate-*r/ 63.8%

         \[\leadsto y + \left(\color{blue}{\frac{-1 \cdot \left(z \cdot \left(y - x\right)\right)}{t}} - -1 \cdot \frac{a \cdot \left(y - x\right)}{t}\right) \]

      3. associate-*r/ 63.8%

         \[\leadsto y + \left(\frac{-1 \cdot \left(z \cdot \left(y - x\right)\right)}{t} - \color{blue}{\frac{-1 \cdot \left(a \cdot \left(y - x\right)\right)}{t}}\right) \]

      4. div-sub 63.8%

         \[\leadsto y + \color{blue}{\frac{-1 \cdot \left(z \cdot \left(y - x\right)\right) - -1 \cdot \left(a \cdot \left(y - x\right)\right)}{t}} \]

      5. distribute-lft-out-- 63.8%

         \[\leadsto y + \frac{\color{blue}{-1 \cdot \left(z \cdot \left(y - x\right) - a \cdot \left(y - x\right)\right)}}{t} \]

      6. associate-*r/ 63.8%

         \[\leadsto y + \color{blue}{-1 \cdot \frac{z \cdot \left(y - x\right) - a \cdot \left(y - x\right)}{t}} \]

      7. mul-1-neg 63.8%

         \[\leadsto y + \color{blue}{\left(-\frac{z \cdot \left(y - x\right) - a \cdot \left(y - x\right)}{t}\right)} \]

      8. unsub-neg 63.8%

         \[\leadsto \color{blue}{y - \frac{z \cdot \left(y - x\right) - a \cdot \left(y - x\right)}{t}} \]

      9. distribute-rgt-out-- 63.8%

         \[\leadsto y - \frac{\color{blue}{\left(y - x\right) \cdot \left(z - a\right)}}{t} \]

      10. associate-/l* 90.3%

          \[\leadsto y - \color{blue}{\frac{y - x}{\frac{t}{z - a}}} \]

   7. Simplified 90.3%

      \[\leadsto \color{blue}{y - \frac{y - x}{\frac{t}{z - a}}} \]

   if -1.50000000000000006e167 < t < 5.80000000000000013e141

   1. Initial program 79.5%

      \[x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \]
   2. Step-by-step derivation

      1. +-commutative 79.5%

         \[\leadsto \color{blue}{\frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} + x} \]

      2. *-commutative 79.5%

         \[\leadsto \frac{\color{blue}{\left(z - t\right) \cdot \left(y - x\right)}}{a - t} + x \]

      3. associate-/l* 82.6%

         \[\leadsto \color{blue}{\frac{z - t}{\frac{a - t}{y - x}}} + x \]

      4. associate-/r/ 91.8%

         \[\leadsto \color{blue}{\frac{z - t}{a - t} \cdot \left(y - x\right)} + x \]

      5. fma-def 91.8%

         \[\leadsto \color{blue}{\mathsf{fma}\left(\frac{z - t}{a - t}, y - x, x\right)} \]

   3. Simplified 91.8%

      \[\leadsto \color{blue}{\mathsf{fma}\left(\frac{z - t}{a - t}, y - x, x\right)} \]
   4. Add Preprocessing
3. Recombined 2 regimes into one program.

4. Final simplification 91.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.5 \cdot 10^{+167} \lor \neg \left(t \leq 5.8 \cdot 10^{+141}\right):\\ \;\;\;\;y + \frac{x - y}{\frac{t}{z - a}}\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(\frac{z - t}{a - t}, y - x, x\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 89.2% accurate, 0.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -3.3 \cdot 10^{+165}:\\ \;\;\;\;\mathsf{fma}\left(z - a, \frac{x}{t}, y\right) + \frac{y}{t} \cdot \left(a - z\right)\\ \mathbf{elif}\;t \leq 7.2 \cdot 10^{+142}:\\ \;\;\;\;\mathsf{fma}\left(\frac{z - t}{a - t}, y - x, x\right)\\ \mathbf{else}:\\ \;\;\;\;y + \frac{x - y}{\frac{t}{z - a}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= t -3.3e+165)
   (+ (fma (- z a) (/ x t) y) (* (/ y t) (- a z)))
   (if (<= t 7.2e+142)
     (fma (/ (- z t) (- a t)) (- y x) x)
     (+ y (/ (- x y) (/ t (- z a)))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= -3.3e+165) {
		tmp = fma((z - a), (x / t), y) + ((y / t) * (a - z));
	} else if (t <= 7.2e+142) {
		tmp = fma(((z - t) / (a - t)), (y - x), x);
	} else {
		tmp = y + ((x - y) / (t / (z - a)));
	}
	return tmp;
}

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (t <= -3.3e+165)
		tmp = Float64(fma(Float64(z - a), Float64(x / t), y) + Float64(Float64(y / t) * Float64(a - z)));
	elseif (t <= 7.2e+142)
		tmp = fma(Float64(Float64(z - t) / Float64(a - t)), Float64(y - x), x);
	else
		tmp = Float64(y + Float64(Float64(x - y) / Float64(t / Float64(z - a))));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[t, -3.3e+165], N[(N[(N[(z - a), $MachinePrecision] * N[(x / t), $MachinePrecision] + y), $MachinePrecision] + N[(N[(y / t), $MachinePrecision] * N[(a - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 7.2e+142], N[(N[(N[(z - t), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision] * N[(y - x), $MachinePrecision] + x), $MachinePrecision], N[(y + N[(N[(x - y), $MachinePrecision] / N[(t / N[(z - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if t < -3.2999999999999999e165

   1. Initial program 18.2%

      \[x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \]
   2. Step-by-step derivation

      1. associate-*l/ 61.9%

         \[\leadsto x + \color{blue}{\frac{y - x}{a - t} \cdot \left(z - t\right)} \]

   3. Simplified 61.9%

      \[\leadsto \color{blue}{x + \frac{y - x}{a - t} \cdot \left(z - t\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in t around inf 52.6%

      \[\leadsto \color{blue}{\left(y + -1 \cdot \frac{z \cdot \left(y - x\right)}{t}\right) - -1 \cdot \frac{a \cdot \left(y - x\right)}{t}} \]
   6. Step-by-step derivation

      1. associate--l+ 52.6%

         \[\leadsto \color{blue}{y + \left(-1 \cdot \frac{z \cdot \left(y - x\right)}{t} - -1 \cdot \frac{a \cdot \left(y - x\right)}{t}\right)} \]

      2. associate-*r/ 52.6%

         \[\leadsto y + \left(\color{blue}{\frac{-1 \cdot \left(z \cdot \left(y - x\right)\right)}{t}} - -1 \cdot \frac{a \cdot \left(y - x\right)}{t}\right) \]

      3. associate-*r/ 52.6%

         \[\leadsto y + \left(\frac{-1 \cdot \left(z \cdot \left(y - x\right)\right)}{t} - \color{blue}{\frac{-1 \cdot \left(a \cdot \left(y - x\right)\right)}{t}}\right) \]

      4. div-sub 52.6%

         \[\leadsto y + \color{blue}{\frac{-1 \cdot \left(z \cdot \left(y - x\right)\right) - -1 \cdot \left(a \cdot \left(y - x\right)\right)}{t}} \]

      5. distribute-lft-out-- 52.6%

         \[\leadsto y + \frac{\color{blue}{-1 \cdot \left(z \cdot \left(y - x\right) - a \cdot \left(y - x\right)\right)}}{t} \]

      6. associate-*r/ 52.6%

         \[\leadsto y + \color{blue}{-1 \cdot \frac{z \cdot \left(y - x\right) - a \cdot \left(y - x\right)}{t}} \]

      7. mul-1-neg 52.6%

         \[\leadsto y + \color{blue}{\left(-\frac{z \cdot \left(y - x\right) - a \cdot \left(y - x\right)}{t}\right)} \]

      8. unsub-neg 52.6%

         \[\leadsto \color{blue}{y - \frac{z \cdot \left(y - x\right) - a \cdot \left(y - x\right)}{t}} \]

      9. distribute-rgt-out-- 52.7%

         \[\leadsto y - \frac{\color{blue}{\left(y - x\right) \cdot \left(z - a\right)}}{t} \]

      10. associate-/l* 83.3%

          \[\leadsto y - \color{blue}{\frac{y - x}{\frac{t}{z - a}}} \]

   7. Simplified 83.3%

      \[\leadsto \color{blue}{y - \frac{y - x}{\frac{t}{z - a}}} \]

   8. Taylor expanded in x around 0 52.2%

      \[\leadsto \color{blue}{\left(y + \frac{x \cdot \left(z - a\right)}{t}\right) - \frac{y \cdot \left(z - a\right)}{t}} \]
   9. Step-by-step derivation

      1. +-commutative 52.2%

         \[\leadsto \color{blue}{\left(\frac{x \cdot \left(z - a\right)}{t} + y\right)} - \frac{y \cdot \left(z - a\right)}{t} \]

      2. *-commutative 52.2%

         \[\leadsto \left(\frac{\color{blue}{\left(z - a\right) \cdot x}}{t} + y\right) - \frac{y \cdot \left(z - a\right)}{t} \]

      3. associate-*r/ 60.5%

         \[\leadsto \left(\color{blue}{\left(z - a\right) \cdot \frac{x}{t}} + y\right) - \frac{y \cdot \left(z - a\right)}{t} \]

      4. fma-def 60.6%

         \[\leadsto \color{blue}{\mathsf{fma}\left(z - a, \frac{x}{t}, y\right)} - \frac{y \cdot \left(z - a\right)}{t} \]

      5. associate-/l* 83.3%

         \[\leadsto \mathsf{fma}\left(z - a, \frac{x}{t}, y\right) - \color{blue}{\frac{y}{\frac{t}{z - a}}} \]

      6. associate-/r/ 83.3%

         \[\leadsto \mathsf{fma}\left(z - a, \frac{x}{t}, y\right) - \color{blue}{\frac{y}{t} \cdot \left(z - a\right)} \]

   10. Simplified 83.3%

       \[\leadsto \color{blue}{\mathsf{fma}\left(z - a, \frac{x}{t}, y\right) - \frac{y}{t} \cdot \left(z - a\right)} \]

   if -3.2999999999999999e165 < t < 7.2000000000000003e142

   1. Initial program 79.5%

      \[x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \]
   2. Step-by-step derivation

      1. +-commutative 79.5%

         \[\leadsto \color{blue}{\frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} + x} \]

      2. *-commutative 79.5%

         \[\leadsto \frac{\color{blue}{\left(z - t\right) \cdot \left(y - x\right)}}{a - t} + x \]

      3. associate-/l* 82.6%

         \[\leadsto \color{blue}{\frac{z - t}{\frac{a - t}{y - x}}} + x \]

      4. associate-/r/ 91.8%

         \[\leadsto \color{blue}{\frac{z - t}{a - t} \cdot \left(y - x\right)} + x \]

      5. fma-def 91.8%

         \[\leadsto \color{blue}{\mathsf{fma}\left(\frac{z - t}{a - t}, y - x, x\right)} \]

   3. Simplified 91.8%

      \[\leadsto \color{blue}{\mathsf{fma}\left(\frac{z - t}{a - t}, y - x, x\right)} \]
   4. Add Preprocessing

   if 7.2000000000000003e142 < t

   1. Initial program 21.6%

      \[x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \]
   2. Step-by-step derivation

      1. associate-*l/ 42.0%

         \[\leadsto x + \color{blue}{\frac{y - x}{a - t} \cdot \left(z - t\right)} \]

   3. Simplified 42.0%

      \[\leadsto \color{blue}{x + \frac{y - x}{a - t} \cdot \left(z - t\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in t around inf 70.8%

      \[\leadsto \color{blue}{\left(y + -1 \cdot \frac{z \cdot \left(y - x\right)}{t}\right) - -1 \cdot \frac{a \cdot \left(y - x\right)}{t}} \]
   6. Step-by-step derivation

      1. associate--l+ 70.8%

         \[\leadsto \color{blue}{y + \left(-1 \cdot \frac{z \cdot \left(y - x\right)}{t} - -1 \cdot \frac{a \cdot \left(y - x\right)}{t}\right)} \]

      2. associate-*r/ 70.8%

         \[\leadsto y + \left(\color{blue}{\frac{-1 \cdot \left(z \cdot \left(y - x\right)\right)}{t}} - -1 \cdot \frac{a \cdot \left(y - x\right)}{t}\right) \]

      3. associate-*r/ 70.8%

         \[\leadsto y + \left(\frac{-1 \cdot \left(z \cdot \left(y - x\right)\right)}{t} - \color{blue}{\frac{-1 \cdot \left(a \cdot \left(y - x\right)\right)}{t}}\right) \]

      4. div-sub 70.8%

         \[\leadsto y + \color{blue}{\frac{-1 \cdot \left(z \cdot \left(y - x\right)\right) - -1 \cdot \left(a \cdot \left(y - x\right)\right)}{t}} \]

      5. distribute-lft-out-- 70.8%

         \[\leadsto y + \frac{\color{blue}{-1 \cdot \left(z \cdot \left(y - x\right) - a \cdot \left(y - x\right)\right)}}{t} \]

      6. associate-*r/ 70.8%

         \[\leadsto y + \color{blue}{-1 \cdot \frac{z \cdot \left(y - x\right) - a \cdot \left(y - x\right)}{t}} \]

      7. mul-1-neg 70.8%

         \[\leadsto y + \color{blue}{\left(-\frac{z \cdot \left(y - x\right) - a \cdot \left(y - x\right)}{t}\right)} \]

      8. unsub-neg 70.8%

         \[\leadsto \color{blue}{y - \frac{z \cdot \left(y - x\right) - a \cdot \left(y - x\right)}{t}} \]

      9. distribute-rgt-out-- 70.8%

         \[\leadsto y - \frac{\color{blue}{\left(y - x\right) \cdot \left(z - a\right)}}{t} \]

      10. associate-/l* 94.7%

          \[\leadsto y - \color{blue}{\frac{y - x}{\frac{t}{z - a}}} \]

   7. Simplified 94.7%

      \[\leadsto \color{blue}{y - \frac{y - x}{\frac{t}{z - a}}} \]
3. Recombined 3 regimes into one program.

4. Final simplification 91.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -3.3 \cdot 10^{+165}:\\ \;\;\;\;\mathsf{fma}\left(z - a, \frac{x}{t}, y\right) + \frac{y}{t} \cdot \left(a - z\right)\\ \mathbf{elif}\;t \leq 7.2 \cdot 10^{+142}:\\ \;\;\;\;\mathsf{fma}\left(\frac{z - t}{a - t}, y - x, x\right)\\ \mathbf{else}:\\ \;\;\;\;y + \frac{x - y}{\frac{t}{z - a}}\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 88.3% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y + \frac{x - y}{\frac{t}{z - a}}\\ t_2 := x + \frac{\left(z - t\right) \cdot \left(y - x\right)}{a - t}\\ \mathbf{if}\;t_2 \leq -\infty:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t_2 \leq -1 \cdot 10^{-234}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t_2 \leq 0:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t_2 \leq 2 \cdot 10^{+290}:\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;x - \left(z - t\right) \cdot \frac{x - y}{a - t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ y (/ (- x y) (/ t (- z a)))))
        (t_2 (+ x (/ (* (- z t) (- y x)) (- a t)))))
   (if (<= t_2 (- INFINITY))
     t_1
     (if (<= t_2 -1e-234)
       t_2
       (if (<= t_2 0.0)
         t_1
         (if (<= t_2 2e+290) t_2 (- x (* (- z t) (/ (- x y) (- a t))))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = y + ((x - y) / (t / (z - a)));
	double t_2 = x + (((z - t) * (y - x)) / (a - t));
	double tmp;
	if (t_2 <= -((double) INFINITY)) {
		tmp = t_1;
	} else if (t_2 <= -1e-234) {
		tmp = t_2;
	} else if (t_2 <= 0.0) {
		tmp = t_1;
	} else if (t_2 <= 2e+290) {
		tmp = t_2;
	} else {
		tmp = x - ((z - t) * ((x - y) / (a - t)));
	}
	return tmp;
}

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = y + ((x - y) / (t / (z - a)));
	double t_2 = x + (((z - t) * (y - x)) / (a - t));
	double tmp;
	if (t_2 <= -Double.POSITIVE_INFINITY) {
		tmp = t_1;
	} else if (t_2 <= -1e-234) {
		tmp = t_2;
	} else if (t_2 <= 0.0) {
		tmp = t_1;
	} else if (t_2 <= 2e+290) {
		tmp = t_2;
	} else {
		tmp = x - ((z - t) * ((x - y) / (a - t)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = y + ((x - y) / (t / (z - a)))
	t_2 = x + (((z - t) * (y - x)) / (a - t))
	tmp = 0
	if t_2 <= -math.inf:
		tmp = t_1
	elif t_2 <= -1e-234:
		tmp = t_2
	elif t_2 <= 0.0:
		tmp = t_1
	elif t_2 <= 2e+290:
		tmp = t_2
	else:
		tmp = x - ((z - t) * ((x - y) / (a - t)))
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(y + Float64(Float64(x - y) / Float64(t / Float64(z - a))))
	t_2 = Float64(x + Float64(Float64(Float64(z - t) * Float64(y - x)) / Float64(a - t)))
	tmp = 0.0
	if (t_2 <= Float64(-Inf))
		tmp = t_1;
	elseif (t_2 <= -1e-234)
		tmp = t_2;
	elseif (t_2 <= 0.0)
		tmp = t_1;
	elseif (t_2 <= 2e+290)
		tmp = t_2;
	else
		tmp = Float64(x - Float64(Float64(z - t) * Float64(Float64(x - y) / Float64(a - t))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = y + ((x - y) / (t / (z - a)));
	t_2 = x + (((z - t) * (y - x)) / (a - t));
	tmp = 0.0;
	if (t_2 <= -Inf)
		tmp = t_1;
	elseif (t_2 <= -1e-234)
		tmp = t_2;
	elseif (t_2 <= 0.0)
		tmp = t_1;
	elseif (t_2 <= 2e+290)
		tmp = t_2;
	else
		tmp = x - ((z - t) * ((x - y) / (a - t)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(y + N[(N[(x - y), $MachinePrecision] / N[(t / N[(z - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x + N[(N[(N[(z - t), $MachinePrecision] * N[(y - x), $MachinePrecision]), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$2, (-Infinity)], t$95$1, If[LessEqual[t$95$2, -1e-234], t$95$2, If[LessEqual[t$95$2, 0.0], t$95$1, If[LessEqual[t$95$2, 2e+290], t$95$2, N[(x - N[(N[(z - t), $MachinePrecision] * N[(N[(x - y), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]

Derivation

1. Split input into 3 regimes

2. if (+.f64 x (/.f64 (*.f64 (-.f64 y x) (-.f64 z t)) (-.f64 a t))) < -inf.0 or -9.9999999999999996e-235 < (+.f64 x (/.f64 (*.f64 (-.f64 y x) (-.f64 z t)) (-.f64 a t))) < 0.0

   1. Initial program 17.3%

      \[x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \]
   2. Step-by-step derivation

      1. associate-*l/ 48.3%

         \[\leadsto x + \color{blue}{\frac{y - x}{a - t} \cdot \left(z - t\right)} \]

   3. Simplified 48.3%

      \[\leadsto \color{blue}{x + \frac{y - x}{a - t} \cdot \left(z - t\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in t around inf 67.2%

      \[\leadsto \color{blue}{\left(y + -1 \cdot \frac{z \cdot \left(y - x\right)}{t}\right) - -1 \cdot \frac{a \cdot \left(y - x\right)}{t}} \]
   6. Step-by-step derivation

      1. associate--l+ 67.2%

         \[\leadsto \color{blue}{y + \left(-1 \cdot \frac{z \cdot \left(y - x\right)}{t} - -1 \cdot \frac{a \cdot \left(y - x\right)}{t}\right)} \]

      2. associate-*r/ 67.2%

         \[\leadsto y + \left(\color{blue}{\frac{-1 \cdot \left(z \cdot \left(y - x\right)\right)}{t}} - -1 \cdot \frac{a \cdot \left(y - x\right)}{t}\right) \]

      3. associate-*r/ 67.2%

         \[\leadsto y + \left(\frac{-1 \cdot \left(z \cdot \left(y - x\right)\right)}{t} - \color{blue}{\frac{-1 \cdot \left(a \cdot \left(y - x\right)\right)}{t}}\right) \]

      4. div-sub 67.2%

         \[\leadsto y + \color{blue}{\frac{-1 \cdot \left(z \cdot \left(y - x\right)\right) - -1 \cdot \left(a \cdot \left(y - x\right)\right)}{t}} \]

      5. distribute-lft-out-- 67.2%

         \[\leadsto y + \frac{\color{blue}{-1 \cdot \left(z \cdot \left(y - x\right) - a \cdot \left(y - x\right)\right)}}{t} \]

      6. associate-*r/ 67.2%

         \[\leadsto y + \color{blue}{-1 \cdot \frac{z \cdot \left(y - x\right) - a \cdot \left(y - x\right)}{t}} \]

      7. mul-1-neg 67.2%

         \[\leadsto y + \color{blue}{\left(-\frac{z \cdot \left(y - x\right) - a \cdot \left(y - x\right)}{t}\right)} \]

      8. unsub-neg 67.2%

         \[\leadsto \color{blue}{y - \frac{z \cdot \left(y - x\right) - a \cdot \left(y - x\right)}{t}} \]

      9. distribute-rgt-out-- 69.0%

         \[\leadsto y - \frac{\color{blue}{\left(y - x\right) \cdot \left(z - a\right)}}{t} \]

      10. associate-/l* 86.9%

          \[\leadsto y - \color{blue}{\frac{y - x}{\frac{t}{z - a}}} \]

   7. Simplified 86.9%

      \[\leadsto \color{blue}{y - \frac{y - x}{\frac{t}{z - a}}} \]

   if -inf.0 < (+.f64 x (/.f64 (*.f64 (-.f64 y x) (-.f64 z t)) (-.f64 a t))) < -9.9999999999999996e-235 or 0.0 < (+.f64 x (/.f64 (*.f64 (-.f64 y x) (-.f64 z t)) (-.f64 a t))) < 2.00000000000000012e290

   1. Initial program 97.0%

      \[x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \]
   2. Add Preprocessing

   if 2.00000000000000012e290 < (+.f64 x (/.f64 (*.f64 (-.f64 y x) (-.f64 z t)) (-.f64 a t)))

   1. Initial program 40.1%

      \[x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \]
   2. Step-by-step derivation

      1. associate-*l/ 84.8%

         \[\leadsto x + \color{blue}{\frac{y - x}{a - t} \cdot \left(z - t\right)} \]

   3. Simplified 84.8%

      \[\leadsto \color{blue}{x + \frac{y - x}{a - t} \cdot \left(z - t\right)} \]
   4. Add Preprocessing
3. Recombined 3 regimes into one program.

4. Final simplification 91.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x + \frac{\left(z - t\right) \cdot \left(y - x\right)}{a - t} \leq -\infty:\\ \;\;\;\;y + \frac{x - y}{\frac{t}{z - a}}\\ \mathbf{elif}\;x + \frac{\left(z - t\right) \cdot \left(y - x\right)}{a - t} \leq -1 \cdot 10^{-234}:\\ \;\;\;\;x + \frac{\left(z - t\right) \cdot \left(y - x\right)}{a - t}\\ \mathbf{elif}\;x + \frac{\left(z - t\right) \cdot \left(y - x\right)}{a - t} \leq 0:\\ \;\;\;\;y + \frac{x - y}{\frac{t}{z - a}}\\ \mathbf{elif}\;x + \frac{\left(z - t\right) \cdot \left(y - x\right)}{a - t} \leq 2 \cdot 10^{+290}:\\ \;\;\;\;x + \frac{\left(z - t\right) \cdot \left(y - x\right)}{a - t}\\ \mathbf{else}:\\ \;\;\;\;x - \left(z - t\right) \cdot \frac{x - y}{a - t}\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 88.3% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + \frac{\left(z - t\right) \cdot \left(y - x\right)}{a - t}\\ \mathbf{if}\;t_1 \leq -\infty:\\ \;\;\;\;y + \frac{x - y}{\frac{t}{z - a}}\\ \mathbf{elif}\;t_1 \leq -1 \cdot 10^{-234}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t_1 \leq 0:\\ \;\;\;\;y + \frac{\left(z - a\right) \cdot \left(x - y\right)}{t}\\ \mathbf{elif}\;t_1 \leq 2 \cdot 10^{+290}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;x - \left(z - t\right) \cdot \frac{x - y}{a - t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ x (/ (* (- z t) (- y x)) (- a t)))))
   (if (<= t_1 (- INFINITY))
     (+ y (/ (- x y) (/ t (- z a))))
     (if (<= t_1 -1e-234)
       t_1
       (if (<= t_1 0.0)
         (+ y (/ (* (- z a) (- x y)) t))
         (if (<= t_1 2e+290) t_1 (- x (* (- z t) (/ (- x y) (- a t))))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x + (((z - t) * (y - x)) / (a - t));
	double tmp;
	if (t_1 <= -((double) INFINITY)) {
		tmp = y + ((x - y) / (t / (z - a)));
	} else if (t_1 <= -1e-234) {
		tmp = t_1;
	} else if (t_1 <= 0.0) {
		tmp = y + (((z - a) * (x - y)) / t);
	} else if (t_1 <= 2e+290) {
		tmp = t_1;
	} else {
		tmp = x - ((z - t) * ((x - y) / (a - t)));
	}
	return tmp;
}

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = x + (((z - t) * (y - x)) / (a - t));
	double tmp;
	if (t_1 <= -Double.POSITIVE_INFINITY) {
		tmp = y + ((x - y) / (t / (z - a)));
	} else if (t_1 <= -1e-234) {
		tmp = t_1;
	} else if (t_1 <= 0.0) {
		tmp = y + (((z - a) * (x - y)) / t);
	} else if (t_1 <= 2e+290) {
		tmp = t_1;
	} else {
		tmp = x - ((z - t) * ((x - y) / (a - t)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x + (((z - t) * (y - x)) / (a - t))
	tmp = 0
	if t_1 <= -math.inf:
		tmp = y + ((x - y) / (t / (z - a)))
	elif t_1 <= -1e-234:
		tmp = t_1
	elif t_1 <= 0.0:
		tmp = y + (((z - a) * (x - y)) / t)
	elif t_1 <= 2e+290:
		tmp = t_1
	else:
		tmp = x - ((z - t) * ((x - y) / (a - t)))
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x + Float64(Float64(Float64(z - t) * Float64(y - x)) / Float64(a - t)))
	tmp = 0.0
	if (t_1 <= Float64(-Inf))
		tmp = Float64(y + Float64(Float64(x - y) / Float64(t / Float64(z - a))));
	elseif (t_1 <= -1e-234)
		tmp = t_1;
	elseif (t_1 <= 0.0)
		tmp = Float64(y + Float64(Float64(Float64(z - a) * Float64(x - y)) / t));
	elseif (t_1 <= 2e+290)
		tmp = t_1;
	else
		tmp = Float64(x - Float64(Float64(z - t) * Float64(Float64(x - y) / Float64(a - t))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x + (((z - t) * (y - x)) / (a - t));
	tmp = 0.0;
	if (t_1 <= -Inf)
		tmp = y + ((x - y) / (t / (z - a)));
	elseif (t_1 <= -1e-234)
		tmp = t_1;
	elseif (t_1 <= 0.0)
		tmp = y + (((z - a) * (x - y)) / t);
	elseif (t_1 <= 2e+290)
		tmp = t_1;
	else
		tmp = x - ((z - t) * ((x - y) / (a - t)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x + N[(N[(N[(z - t), $MachinePrecision] * N[(y - x), $MachinePrecision]), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, (-Infinity)], N[(y + N[(N[(x - y), $MachinePrecision] / N[(t / N[(z - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, -1e-234], t$95$1, If[LessEqual[t$95$1, 0.0], N[(y + N[(N[(N[(z - a), $MachinePrecision] * N[(x - y), $MachinePrecision]), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, 2e+290], t$95$1, N[(x - N[(N[(z - t), $MachinePrecision] * N[(N[(x - y), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 4 regimes

2. if (+.f64 x (/.f64 (*.f64 (-.f64 y x) (-.f64 z t)) (-.f64 a t))) < -inf.0

   1. Initial program 24.0%

      \[x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \]
   2. Step-by-step derivation

      1. associate-*l/ 71.1%

         \[\leadsto x + \color{blue}{\frac{y - x}{a - t} \cdot \left(z - t\right)} \]

   3. Simplified 71.1%

      \[\leadsto \color{blue}{x + \frac{y - x}{a - t} \cdot \left(z - t\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in t around inf 50.6%

      \[\leadsto \color{blue}{\left(y + -1 \cdot \frac{z \cdot \left(y - x\right)}{t}\right) - -1 \cdot \frac{a \cdot \left(y - x\right)}{t}} \]
   6. Step-by-step derivation

      1. associate--l+ 50.6%

         \[\leadsto \color{blue}{y + \left(-1 \cdot \frac{z \cdot \left(y - x\right)}{t} - -1 \cdot \frac{a \cdot \left(y - x\right)}{t}\right)} \]

      2. associate-*r/ 50.6%

         \[\leadsto y + \left(\color{blue}{\frac{-1 \cdot \left(z \cdot \left(y - x\right)\right)}{t}} - -1 \cdot \frac{a \cdot \left(y - x\right)}{t}\right) \]

      3. associate-*r/ 50.6%

         \[\leadsto y + \left(\frac{-1 \cdot \left(z \cdot \left(y - x\right)\right)}{t} - \color{blue}{\frac{-1 \cdot \left(a \cdot \left(y - x\right)\right)}{t}}\right) \]

      4. div-sub 50.6%

         \[\leadsto y + \color{blue}{\frac{-1 \cdot \left(z \cdot \left(y - x\right)\right) - -1 \cdot \left(a \cdot \left(y - x\right)\right)}{t}} \]

      5. distribute-lft-out-- 50.6%

         \[\leadsto y + \frac{\color{blue}{-1 \cdot \left(z \cdot \left(y - x\right) - a \cdot \left(y - x\right)\right)}}{t} \]

      6. associate-*r/ 50.6%

         \[\leadsto y + \color{blue}{-1 \cdot \frac{z \cdot \left(y - x\right) - a \cdot \left(y - x\right)}{t}} \]

      7. mul-1-neg 50.6%

         \[\leadsto y + \color{blue}{\left(-\frac{z \cdot \left(y - x\right) - a \cdot \left(y - x\right)}{t}\right)} \]

      8. unsub-neg 50.6%

         \[\leadsto \color{blue}{y - \frac{z \cdot \left(y - x\right) - a \cdot \left(y - x\right)}{t}} \]

      9. distribute-rgt-out-- 53.1%

         \[\leadsto y - \frac{\color{blue}{\left(y - x\right) \cdot \left(z - a\right)}}{t} \]

      10. associate-/l* 80.4%

          \[\leadsto y - \color{blue}{\frac{y - x}{\frac{t}{z - a}}} \]

   7. Simplified 80.4%

      \[\leadsto \color{blue}{y - \frac{y - x}{\frac{t}{z - a}}} \]

   if -inf.0 < (+.f64 x (/.f64 (*.f64 (-.f64 y x) (-.f64 z t)) (-.f64 a t))) < -9.9999999999999996e-235 or 0.0 < (+.f64 x (/.f64 (*.f64 (-.f64 y x) (-.f64 z t)) (-.f64 a t))) < 2.00000000000000012e290

   1. Initial program 97.0%

      \[x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \]
   2. Add Preprocessing

   if -9.9999999999999996e-235 < (+.f64 x (/.f64 (*.f64 (-.f64 y x) (-.f64 z t)) (-.f64 a t))) < 0.0

   1. Initial program 4.2%

      \[x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \]
   2. Step-by-step derivation

      1. +-commutative 4.2%

         \[\leadsto \color{blue}{\frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} + x} \]

      2. *-commutative 4.2%

         \[\leadsto \frac{\color{blue}{\left(z - t\right) \cdot \left(y - x\right)}}{a - t} + x \]

      3. associate-/l* 3.6%

         \[\leadsto \color{blue}{\frac{z - t}{\frac{a - t}{y - x}}} + x \]

      4. associate-/r/ 4.2%

         \[\leadsto \color{blue}{\frac{z - t}{a - t} \cdot \left(y - x\right)} + x \]

      5. fma-def 4.2%

         \[\leadsto \color{blue}{\mathsf{fma}\left(\frac{z - t}{a - t}, y - x, x\right)} \]

   3. Simplified 4.2%

      \[\leadsto \color{blue}{\mathsf{fma}\left(\frac{z - t}{a - t}, y - x, x\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in t around -inf 99.9%

      \[\leadsto \color{blue}{y + -1 \cdot \frac{\left(y - x\right) \cdot \left(z - a\right)}{t}} \]

   if 2.00000000000000012e290 < (+.f64 x (/.f64 (*.f64 (-.f64 y x) (-.f64 z t)) (-.f64 a t)))

   1. Initial program 40.1%

      \[x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \]
   2. Step-by-step derivation

      1. associate-*l/ 84.8%

         \[\leadsto x + \color{blue}{\frac{y - x}{a - t} \cdot \left(z - t\right)} \]

   3. Simplified 84.8%

      \[\leadsto \color{blue}{x + \frac{y - x}{a - t} \cdot \left(z - t\right)} \]
   4. Add Preprocessing
3. Recombined 4 regimes into one program.

4. Final simplification 91.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x + \frac{\left(z - t\right) \cdot \left(y - x\right)}{a - t} \leq -\infty:\\ \;\;\;\;y + \frac{x - y}{\frac{t}{z - a}}\\ \mathbf{elif}\;x + \frac{\left(z - t\right) \cdot \left(y - x\right)}{a - t} \leq -1 \cdot 10^{-234}:\\ \;\;\;\;x + \frac{\left(z - t\right) \cdot \left(y - x\right)}{a - t}\\ \mathbf{elif}\;x + \frac{\left(z - t\right) \cdot \left(y - x\right)}{a - t} \leq 0:\\ \;\;\;\;y + \frac{\left(z - a\right) \cdot \left(x - y\right)}{t}\\ \mathbf{elif}\;x + \frac{\left(z - t\right) \cdot \left(y - x\right)}{a - t} \leq 2 \cdot 10^{+290}:\\ \;\;\;\;x + \frac{\left(z - t\right) \cdot \left(y - x\right)}{a - t}\\ \mathbf{else}:\\ \;\;\;\;x - \left(z - t\right) \cdot \frac{x - y}{a - t}\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 63.1% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y \cdot \frac{z - t}{a - t}\\ t_2 := x - \frac{y}{a} \cdot \left(t - z\right)\\ t_3 := z \cdot \frac{y - x}{a - t}\\ \mathbf{if}\;a \leq -1.15 \cdot 10^{+92}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;a \leq -4 \cdot 10^{-112}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq -4.1 \cdot 10^{-202}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;a \leq 1.35 \cdot 10^{+31}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq 6.2 \cdot 10^{+83}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;a \leq 6.4 \cdot 10^{+83}:\\ \;\;\;\;y\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* y (/ (- z t) (- a t))))
        (t_2 (- x (* (/ y a) (- t z))))
        (t_3 (* z (/ (- y x) (- a t)))))
   (if (<= a -1.15e+92)
     t_2
     (if (<= a -4e-112)
       t_1
       (if (<= a -4.1e-202)
         t_3
         (if (<= a 1.35e+31)
           t_1
           (if (<= a 6.2e+83) t_3 (if (<= a 6.4e+83) y t_2))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = y * ((z - t) / (a - t));
	double t_2 = x - ((y / a) * (t - z));
	double t_3 = z * ((y - x) / (a - t));
	double tmp;
	if (a <= -1.15e+92) {
		tmp = t_2;
	} else if (a <= -4e-112) {
		tmp = t_1;
	} else if (a <= -4.1e-202) {
		tmp = t_3;
	} else if (a <= 1.35e+31) {
		tmp = t_1;
	} else if (a <= 6.2e+83) {
		tmp = t_3;
	} else if (a <= 6.4e+83) {
		tmp = y;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: tmp
    t_1 = y * ((z - t) / (a - t))
    t_2 = x - ((y / a) * (t - z))
    t_3 = z * ((y - x) / (a - t))
    if (a <= (-1.15d+92)) then
        tmp = t_2
    else if (a <= (-4d-112)) then
        tmp = t_1
    else if (a <= (-4.1d-202)) then
        tmp = t_3
    else if (a <= 1.35d+31) then
        tmp = t_1
    else if (a <= 6.2d+83) then
        tmp = t_3
    else if (a <= 6.4d+83) then
        tmp = y
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = y * ((z - t) / (a - t));
	double t_2 = x - ((y / a) * (t - z));
	double t_3 = z * ((y - x) / (a - t));
	double tmp;
	if (a <= -1.15e+92) {
		tmp = t_2;
	} else if (a <= -4e-112) {
		tmp = t_1;
	} else if (a <= -4.1e-202) {
		tmp = t_3;
	} else if (a <= 1.35e+31) {
		tmp = t_1;
	} else if (a <= 6.2e+83) {
		tmp = t_3;
	} else if (a <= 6.4e+83) {
		tmp = y;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = y * ((z - t) / (a - t))
	t_2 = x - ((y / a) * (t - z))
	t_3 = z * ((y - x) / (a - t))
	tmp = 0
	if a <= -1.15e+92:
		tmp = t_2
	elif a <= -4e-112:
		tmp = t_1
	elif a <= -4.1e-202:
		tmp = t_3
	elif a <= 1.35e+31:
		tmp = t_1
	elif a <= 6.2e+83:
		tmp = t_3
	elif a <= 6.4e+83:
		tmp = y
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(y * Float64(Float64(z - t) / Float64(a - t)))
	t_2 = Float64(x - Float64(Float64(y / a) * Float64(t - z)))
	t_3 = Float64(z * Float64(Float64(y - x) / Float64(a - t)))
	tmp = 0.0
	if (a <= -1.15e+92)
		tmp = t_2;
	elseif (a <= -4e-112)
		tmp = t_1;
	elseif (a <= -4.1e-202)
		tmp = t_3;
	elseif (a <= 1.35e+31)
		tmp = t_1;
	elseif (a <= 6.2e+83)
		tmp = t_3;
	elseif (a <= 6.4e+83)
		tmp = y;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = y * ((z - t) / (a - t));
	t_2 = x - ((y / a) * (t - z));
	t_3 = z * ((y - x) / (a - t));
	tmp = 0.0;
	if (a <= -1.15e+92)
		tmp = t_2;
	elseif (a <= -4e-112)
		tmp = t_1;
	elseif (a <= -4.1e-202)
		tmp = t_3;
	elseif (a <= 1.35e+31)
		tmp = t_1;
	elseif (a <= 6.2e+83)
		tmp = t_3;
	elseif (a <= 6.4e+83)
		tmp = y;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(y * N[(N[(z - t), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x - N[(N[(y / a), $MachinePrecision] * N[(t - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(z * N[(N[(y - x), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -1.15e+92], t$95$2, If[LessEqual[a, -4e-112], t$95$1, If[LessEqual[a, -4.1e-202], t$95$3, If[LessEqual[a, 1.35e+31], t$95$1, If[LessEqual[a, 6.2e+83], t$95$3, If[LessEqual[a, 6.4e+83], y, t$95$2]]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if a < -1.14999999999999999e92 or 6.3999999999999998e83 < a

   1. Initial program 70.4%

      \[x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \]
   2. Step-by-step derivation

      1. associate-*l/ 89.0%

         \[\leadsto x + \color{blue}{\frac{y - x}{a - t} \cdot \left(z - t\right)} \]

   3. Simplified 89.0%

      \[\leadsto \color{blue}{x + \frac{y - x}{a - t} \cdot \left(z - t\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in a around inf 67.6%

      \[\leadsto \color{blue}{x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a}} \]
   6. Step-by-step derivation

      1. associate-/l* 86.7%

         \[\leadsto x + \color{blue}{\frac{y - x}{\frac{a}{z - t}}} \]

   7. Simplified 86.7%

      \[\leadsto \color{blue}{x + \frac{y - x}{\frac{a}{z - t}}} \]

   8. Taylor expanded in y around inf 73.2%

      \[\leadsto x + \color{blue}{\frac{y \cdot \left(z - t\right)}{a}} \]
   9. Step-by-step derivation

      1. associate-/l* 81.9%

         \[\leadsto x + \color{blue}{\frac{y}{\frac{a}{z - t}}} \]

      2. associate-/r/ 78.8%

         \[\leadsto x + \color{blue}{\frac{y}{a} \cdot \left(z - t\right)} \]

   10. Simplified 78.8%

       \[\leadsto x + \color{blue}{\frac{y}{a} \cdot \left(z - t\right)} \]

   if -1.14999999999999999e92 < a < -3.9999999999999998e-112 or -4.1000000000000004e-202 < a < 1.34999999999999993e31

   1. Initial program 61.1%

      \[x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \]
   2. Step-by-step derivation

      1. +-commutative 61.1%

         \[\leadsto \color{blue}{\frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} + x} \]

      2. associate-*l/ 67.5%

         \[\leadsto \color{blue}{\frac{y - x}{a - t} \cdot \left(z - t\right)} + x \]

      3. fma-def 67.7%

         \[\leadsto \color{blue}{\mathsf{fma}\left(\frac{y - x}{a - t}, z - t, x\right)} \]

   3. Simplified 67.7%

      \[\leadsto \color{blue}{\mathsf{fma}\left(\frac{y - x}{a - t}, z - t, x\right)} \]
   4. Add Preprocessing
   5. Step-by-step derivation

      1. fma-udef 67.5%

         \[\leadsto \color{blue}{\frac{y - x}{a - t} \cdot \left(z - t\right) + x} \]

      2. associate-/r/ 77.4%

         \[\leadsto \color{blue}{\frac{y - x}{\frac{a - t}{z - t}}} + x \]

      3. div-inv 77.4%

         \[\leadsto \color{blue}{\left(y - x\right) \cdot \frac{1}{\frac{a - t}{z - t}}} + x \]

      4. clear-num 77.4%

         \[\leadsto \left(y - x\right) \cdot \color{blue}{\frac{z - t}{a - t}} + x \]

   6. Applied egg-rr 77.4%

      \[\leadsto \color{blue}{\left(y - x\right) \cdot \frac{z - t}{a - t} + x} \]

   7. Taylor expanded in y around inf 69.7%

      \[\leadsto \color{blue}{y \cdot \left(\frac{z}{a - t} - \frac{t}{a - t}\right)} \]
   8. Step-by-step derivation

      1. div-sub 69.7%

         \[\leadsto y \cdot \color{blue}{\frac{z - t}{a - t}} \]

   9. Simplified 69.7%

      \[\leadsto \color{blue}{y \cdot \frac{z - t}{a - t}} \]

   if -3.9999999999999998e-112 < a < -4.1000000000000004e-202 or 1.34999999999999993e31 < a < 6.19999999999999984e83

   1. Initial program 62.9%

      \[x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \]
   2. Step-by-step derivation

      1. associate-*l/ 57.4%

         \[\leadsto x + \color{blue}{\frac{y - x}{a - t} \cdot \left(z - t\right)} \]

   3. Simplified 57.4%

      \[\leadsto \color{blue}{x + \frac{y - x}{a - t} \cdot \left(z - t\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in z around inf 78.3%

      \[\leadsto \color{blue}{z \cdot \left(\frac{y}{a - t} - \frac{x}{a - t}\right)} \]
   6. Step-by-step derivation

      1. div-sub 78.3%

         \[\leadsto z \cdot \color{blue}{\frac{y - x}{a - t}} \]

   7. Simplified 78.3%

      \[\leadsto \color{blue}{z \cdot \frac{y - x}{a - t}} \]

   if 6.19999999999999984e83 < a < 6.3999999999999998e83

   1. Initial program 9.9%

      \[x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \]
   2. Step-by-step derivation

      1. associate-*l/ 100.0%

         \[\leadsto x + \color{blue}{\frac{y - x}{a - t} \cdot \left(z - t\right)} \]

   3. Simplified 100.0%

      \[\leadsto \color{blue}{x + \frac{y - x}{a - t} \cdot \left(z - t\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in t around inf 100.0%

      \[\leadsto \color{blue}{y} \]
3. Recombined 4 regimes into one program.

4. Final simplification 74.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -1.15 \cdot 10^{+92}:\\ \;\;\;\;x - \frac{y}{a} \cdot \left(t - z\right)\\ \mathbf{elif}\;a \leq -4 \cdot 10^{-112}:\\ \;\;\;\;y \cdot \frac{z - t}{a - t}\\ \mathbf{elif}\;a \leq -4.1 \cdot 10^{-202}:\\ \;\;\;\;z \cdot \frac{y - x}{a - t}\\ \mathbf{elif}\;a \leq 1.35 \cdot 10^{+31}:\\ \;\;\;\;y \cdot \frac{z - t}{a - t}\\ \mathbf{elif}\;a \leq 6.2 \cdot 10^{+83}:\\ \;\;\;\;z \cdot \frac{y - x}{a - t}\\ \mathbf{elif}\;a \leq 6.4 \cdot 10^{+83}:\\ \;\;\;\;y\\ \mathbf{else}:\\ \;\;\;\;x - \frac{y}{a} \cdot \left(t - z\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 49.1% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{z}{\frac{t}{x - y}}\\ t_2 := x + \frac{y}{\frac{a}{z}}\\ \mathbf{if}\;a \leq -5 \cdot 10^{-57}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;a \leq -7 \cdot 10^{-110}:\\ \;\;\;\;y\\ \mathbf{elif}\;a \leq -2.05 \cdot 10^{-144}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq -1.1 \cdot 10^{-219}:\\ \;\;\;\;\frac{-x}{\frac{a - t}{z}}\\ \mathbf{elif}\;a \leq 1.8 \cdot 10^{-119}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq 9.5 \cdot 10^{+27}:\\ \;\;\;\;y\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (/ z (/ t (- x y)))) (t_2 (+ x (/ y (/ a z)))))
   (if (<= a -5e-57)
     t_2
     (if (<= a -7e-110)
       y
       (if (<= a -2.05e-144)
         t_1
         (if (<= a -1.1e-219)
           (/ (- x) (/ (- a t) z))
           (if (<= a 1.8e-119) t_1 (if (<= a 9.5e+27) y t_2))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = z / (t / (x - y));
	double t_2 = x + (y / (a / z));
	double tmp;
	if (a <= -5e-57) {
		tmp = t_2;
	} else if (a <= -7e-110) {
		tmp = y;
	} else if (a <= -2.05e-144) {
		tmp = t_1;
	} else if (a <= -1.1e-219) {
		tmp = -x / ((a - t) / z);
	} else if (a <= 1.8e-119) {
		tmp = t_1;
	} else if (a <= 9.5e+27) {
		tmp = y;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = z / (t / (x - y))
    t_2 = x + (y / (a / z))
    if (a <= (-5d-57)) then
        tmp = t_2
    else if (a <= (-7d-110)) then
        tmp = y
    else if (a <= (-2.05d-144)) then
        tmp = t_1
    else if (a <= (-1.1d-219)) then
        tmp = -x / ((a - t) / z)
    else if (a <= 1.8d-119) then
        tmp = t_1
    else if (a <= 9.5d+27) then
        tmp = y
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = z / (t / (x - y));
	double t_2 = x + (y / (a / z));
	double tmp;
	if (a <= -5e-57) {
		tmp = t_2;
	} else if (a <= -7e-110) {
		tmp = y;
	} else if (a <= -2.05e-144) {
		tmp = t_1;
	} else if (a <= -1.1e-219) {
		tmp = -x / ((a - t) / z);
	} else if (a <= 1.8e-119) {
		tmp = t_1;
	} else if (a <= 9.5e+27) {
		tmp = y;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = z / (t / (x - y))
	t_2 = x + (y / (a / z))
	tmp = 0
	if a <= -5e-57:
		tmp = t_2
	elif a <= -7e-110:
		tmp = y
	elif a <= -2.05e-144:
		tmp = t_1
	elif a <= -1.1e-219:
		tmp = -x / ((a - t) / z)
	elif a <= 1.8e-119:
		tmp = t_1
	elif a <= 9.5e+27:
		tmp = y
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(z / Float64(t / Float64(x - y)))
	t_2 = Float64(x + Float64(y / Float64(a / z)))
	tmp = 0.0
	if (a <= -5e-57)
		tmp = t_2;
	elseif (a <= -7e-110)
		tmp = y;
	elseif (a <= -2.05e-144)
		tmp = t_1;
	elseif (a <= -1.1e-219)
		tmp = Float64(Float64(-x) / Float64(Float64(a - t) / z));
	elseif (a <= 1.8e-119)
		tmp = t_1;
	elseif (a <= 9.5e+27)
		tmp = y;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = z / (t / (x - y));
	t_2 = x + (y / (a / z));
	tmp = 0.0;
	if (a <= -5e-57)
		tmp = t_2;
	elseif (a <= -7e-110)
		tmp = y;
	elseif (a <= -2.05e-144)
		tmp = t_1;
	elseif (a <= -1.1e-219)
		tmp = -x / ((a - t) / z);
	elseif (a <= 1.8e-119)
		tmp = t_1;
	elseif (a <= 9.5e+27)
		tmp = y;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(z / N[(t / N[(x - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x + N[(y / N[(a / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -5e-57], t$95$2, If[LessEqual[a, -7e-110], y, If[LessEqual[a, -2.05e-144], t$95$1, If[LessEqual[a, -1.1e-219], N[((-x) / N[(N[(a - t), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 1.8e-119], t$95$1, If[LessEqual[a, 9.5e+27], y, t$95$2]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if a < -5.0000000000000002e-57 or 9.4999999999999997e27 < a

   1. Initial program 65.9%

      \[x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \]
   2. Step-by-step derivation

      1. associate-*l/ 82.7%

         \[\leadsto x + \color{blue}{\frac{y - x}{a - t} \cdot \left(z - t\right)} \]

   3. Simplified 82.7%

      \[\leadsto \color{blue}{x + \frac{y - x}{a - t} \cdot \left(z - t\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in t around 0 62.0%

      \[\leadsto \color{blue}{x + \frac{z \cdot \left(y - x\right)}{a}} \]

   6. Taylor expanded in y around inf 58.6%

      \[\leadsto x + \color{blue}{\frac{y \cdot z}{a}} \]
   7. Step-by-step derivation

      1. associate-/l* 63.7%

         \[\leadsto x + \color{blue}{\frac{y}{\frac{a}{z}}} \]

   8. Simplified 63.7%

      \[\leadsto x + \color{blue}{\frac{y}{\frac{a}{z}}} \]

   if -5.0000000000000002e-57 < a < -6.99999999999999947e-110 or 1.8e-119 < a < 9.4999999999999997e27

   1. Initial program 53.4%

      \[x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \]
   2. Step-by-step derivation

      1. associate-*l/ 72.6%

         \[\leadsto x + \color{blue}{\frac{y - x}{a - t} \cdot \left(z - t\right)} \]

   3. Simplified 72.6%

      \[\leadsto \color{blue}{x + \frac{y - x}{a - t} \cdot \left(z - t\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in t around inf 54.8%

      \[\leadsto \color{blue}{y} \]

   if -6.99999999999999947e-110 < a < -2.05e-144 or -1.1e-219 < a < 1.8e-119

   1. Initial program 70.6%

      \[x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \]
   2. Step-by-step derivation

      1. associate-*l/ 64.7%

         \[\leadsto x + \color{blue}{\frac{y - x}{a - t} \cdot \left(z - t\right)} \]

   3. Simplified 64.7%

      \[\leadsto \color{blue}{x + \frac{y - x}{a - t} \cdot \left(z - t\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in t around inf 75.1%

      \[\leadsto \color{blue}{\left(y + -1 \cdot \frac{z \cdot \left(y - x\right)}{t}\right) - -1 \cdot \frac{a \cdot \left(y - x\right)}{t}} \]
   6. Step-by-step derivation

      1. associate--l+ 75.1%

         \[\leadsto \color{blue}{y + \left(-1 \cdot \frac{z \cdot \left(y - x\right)}{t} - -1 \cdot \frac{a \cdot \left(y - x\right)}{t}\right)} \]

      2. associate-*r/ 75.1%

         \[\leadsto y + \left(\color{blue}{\frac{-1 \cdot \left(z \cdot \left(y - x\right)\right)}{t}} - -1 \cdot \frac{a \cdot \left(y - x\right)}{t}\right) \]

      3. associate-*r/ 75.1%

         \[\leadsto y + \left(\frac{-1 \cdot \left(z \cdot \left(y - x\right)\right)}{t} - \color{blue}{\frac{-1 \cdot \left(a \cdot \left(y - x\right)\right)}{t}}\right) \]

      4. div-sub 75.1%

         \[\leadsto y + \color{blue}{\frac{-1 \cdot \left(z \cdot \left(y - x\right)\right) - -1 \cdot \left(a \cdot \left(y - x\right)\right)}{t}} \]

      5. distribute-lft-out-- 75.1%

         \[\leadsto y + \frac{\color{blue}{-1 \cdot \left(z \cdot \left(y - x\right) - a \cdot \left(y - x\right)\right)}}{t} \]

      6. associate-*r/ 75.1%

         \[\leadsto y + \color{blue}{-1 \cdot \frac{z \cdot \left(y - x\right) - a \cdot \left(y - x\right)}{t}} \]

      7. mul-1-neg 75.1%

         \[\leadsto y + \color{blue}{\left(-\frac{z \cdot \left(y - x\right) - a \cdot \left(y - x\right)}{t}\right)} \]

      8. unsub-neg 75.1%

         \[\leadsto \color{blue}{y - \frac{z \cdot \left(y - x\right) - a \cdot \left(y - x\right)}{t}} \]

      9. distribute-rgt-out-- 75.1%

         \[\leadsto y - \frac{\color{blue}{\left(y - x\right) \cdot \left(z - a\right)}}{t} \]

      10. associate-/l* 87.7%

          \[\leadsto y - \color{blue}{\frac{y - x}{\frac{t}{z - a}}} \]

   7. Simplified 87.7%

      \[\leadsto \color{blue}{y - \frac{y - x}{\frac{t}{z - a}}} \]

   8. Taylor expanded in z around -inf 46.9%

      \[\leadsto \color{blue}{-1 \cdot \frac{z \cdot \left(y - x\right)}{t}} \]
   9. Step-by-step derivation

      1. associate-*r/ 46.9%

         \[\leadsto \color{blue}{\frac{-1 \cdot \left(z \cdot \left(y - x\right)\right)}{t}} \]

      2. mul-1-neg 46.9%

         \[\leadsto \frac{\color{blue}{-z \cdot \left(y - x\right)}}{t} \]

   10. Simplified 46.9%

       \[\leadsto \color{blue}{\frac{-z \cdot \left(y - x\right)}{t}} \]

   11. Taylor expanded in z around inf 46.9%

       \[\leadsto \color{blue}{\frac{z \cdot \left(x - y\right)}{t}} \]
   12. Step-by-step derivation

       1. associate-/l* 54.2%

          \[\leadsto \color{blue}{\frac{z}{\frac{t}{x - y}}} \]

   13. Simplified 54.2%

       \[\leadsto \color{blue}{\frac{z}{\frac{t}{x - y}}} \]

   if -2.05e-144 < a < -1.1e-219

   1. Initial program 53.5%

      \[x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \]
   2. Step-by-step derivation

      1. associate-*l/ 52.9%

         \[\leadsto x + \color{blue}{\frac{y - x}{a - t} \cdot \left(z - t\right)} \]

   3. Simplified 52.9%

      \[\leadsto \color{blue}{x + \frac{y - x}{a - t} \cdot \left(z - t\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in x around -inf 68.0%

      \[\leadsto \color{blue}{-1 \cdot \left(x \cdot \left(\frac{z}{a - t} - \left(1 + \frac{t}{a - t}\right)\right)\right)} \]
   6. Step-by-step derivation

      1. associate-*r* 68.0%

         \[\leadsto \color{blue}{\left(-1 \cdot x\right) \cdot \left(\frac{z}{a - t} - \left(1 + \frac{t}{a - t}\right)\right)} \]

      2. neg-mul-1 68.0%

         \[\leadsto \color{blue}{\left(-x\right)} \cdot \left(\frac{z}{a - t} - \left(1 + \frac{t}{a - t}\right)\right) \]

   7. Simplified 68.0%

      \[\leadsto \color{blue}{\left(-x\right) \cdot \left(\frac{z}{a - t} - \left(1 + \frac{t}{a - t}\right)\right)} \]

   8. Taylor expanded in z around inf 68.4%

      \[\leadsto \color{blue}{-1 \cdot \frac{x \cdot z}{a - t}} \]
   9. Step-by-step derivation

      1. mul-1-neg 68.4%

         \[\leadsto \color{blue}{-\frac{x \cdot z}{a - t}} \]

      2. associate-/l* 68.2%

         \[\leadsto -\color{blue}{\frac{x}{\frac{a - t}{z}}} \]

   10. Simplified 68.2%

       \[\leadsto \color{blue}{-\frac{x}{\frac{a - t}{z}}} \]
3. Recombined 4 regimes into one program.

4. Final simplification 60.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -5 \cdot 10^{-57}:\\ \;\;\;\;x + \frac{y}{\frac{a}{z}}\\ \mathbf{elif}\;a \leq -7 \cdot 10^{-110}:\\ \;\;\;\;y\\ \mathbf{elif}\;a \leq -2.05 \cdot 10^{-144}:\\ \;\;\;\;\frac{z}{\frac{t}{x - y}}\\ \mathbf{elif}\;a \leq -1.1 \cdot 10^{-219}:\\ \;\;\;\;\frac{-x}{\frac{a - t}{z}}\\ \mathbf{elif}\;a \leq 1.8 \cdot 10^{-119}:\\ \;\;\;\;\frac{z}{\frac{t}{x - y}}\\ \mathbf{elif}\;a \leq 9.5 \cdot 10^{+27}:\\ \;\;\;\;y\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{\frac{a}{z}}\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 60.2% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y \cdot \frac{z - t}{a - t}\\ t_2 := x + \frac{y}{\frac{a}{z}}\\ t_3 := z \cdot \frac{y - x}{a - t}\\ \mathbf{if}\;a \leq -3.5 \cdot 10^{+100}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;a \leq -3.7 \cdot 10^{-112}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq -2.4 \cdot 10^{-200}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;a \leq 4.8 \cdot 10^{+31}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq 6.2 \cdot 10^{+83}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;a \leq 6.4 \cdot 10^{+83}:\\ \;\;\;\;y\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* y (/ (- z t) (- a t))))
        (t_2 (+ x (/ y (/ a z))))
        (t_3 (* z (/ (- y x) (- a t)))))
   (if (<= a -3.5e+100)
     t_2
     (if (<= a -3.7e-112)
       t_1
       (if (<= a -2.4e-200)
         t_3
         (if (<= a 4.8e+31)
           t_1
           (if (<= a 6.2e+83) t_3 (if (<= a 6.4e+83) y t_2))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = y * ((z - t) / (a - t));
	double t_2 = x + (y / (a / z));
	double t_3 = z * ((y - x) / (a - t));
	double tmp;
	if (a <= -3.5e+100) {
		tmp = t_2;
	} else if (a <= -3.7e-112) {
		tmp = t_1;
	} else if (a <= -2.4e-200) {
		tmp = t_3;
	} else if (a <= 4.8e+31) {
		tmp = t_1;
	} else if (a <= 6.2e+83) {
		tmp = t_3;
	} else if (a <= 6.4e+83) {
		tmp = y;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: tmp
    t_1 = y * ((z - t) / (a - t))
    t_2 = x + (y / (a / z))
    t_3 = z * ((y - x) / (a - t))
    if (a <= (-3.5d+100)) then
        tmp = t_2
    else if (a <= (-3.7d-112)) then
        tmp = t_1
    else if (a <= (-2.4d-200)) then
        tmp = t_3
    else if (a <= 4.8d+31) then
        tmp = t_1
    else if (a <= 6.2d+83) then
        tmp = t_3
    else if (a <= 6.4d+83) then
        tmp = y
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = y * ((z - t) / (a - t));
	double t_2 = x + (y / (a / z));
	double t_3 = z * ((y - x) / (a - t));
	double tmp;
	if (a <= -3.5e+100) {
		tmp = t_2;
	} else if (a <= -3.7e-112) {
		tmp = t_1;
	} else if (a <= -2.4e-200) {
		tmp = t_3;
	} else if (a <= 4.8e+31) {
		tmp = t_1;
	} else if (a <= 6.2e+83) {
		tmp = t_3;
	} else if (a <= 6.4e+83) {
		tmp = y;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = y * ((z - t) / (a - t))
	t_2 = x + (y / (a / z))
	t_3 = z * ((y - x) / (a - t))
	tmp = 0
	if a <= -3.5e+100:
		tmp = t_2
	elif a <= -3.7e-112:
		tmp = t_1
	elif a <= -2.4e-200:
		tmp = t_3
	elif a <= 4.8e+31:
		tmp = t_1
	elif a <= 6.2e+83:
		tmp = t_3
	elif a <= 6.4e+83:
		tmp = y
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(y * Float64(Float64(z - t) / Float64(a - t)))
	t_2 = Float64(x + Float64(y / Float64(a / z)))
	t_3 = Float64(z * Float64(Float64(y - x) / Float64(a - t)))
	tmp = 0.0
	if (a <= -3.5e+100)
		tmp = t_2;
	elseif (a <= -3.7e-112)
		tmp = t_1;
	elseif (a <= -2.4e-200)
		tmp = t_3;
	elseif (a <= 4.8e+31)
		tmp = t_1;
	elseif (a <= 6.2e+83)
		tmp = t_3;
	elseif (a <= 6.4e+83)
		tmp = y;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = y * ((z - t) / (a - t));
	t_2 = x + (y / (a / z));
	t_3 = z * ((y - x) / (a - t));
	tmp = 0.0;
	if (a <= -3.5e+100)
		tmp = t_2;
	elseif (a <= -3.7e-112)
		tmp = t_1;
	elseif (a <= -2.4e-200)
		tmp = t_3;
	elseif (a <= 4.8e+31)
		tmp = t_1;
	elseif (a <= 6.2e+83)
		tmp = t_3;
	elseif (a <= 6.4e+83)
		tmp = y;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(y * N[(N[(z - t), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x + N[(y / N[(a / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(z * N[(N[(y - x), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -3.5e+100], t$95$2, If[LessEqual[a, -3.7e-112], t$95$1, If[LessEqual[a, -2.4e-200], t$95$3, If[LessEqual[a, 4.8e+31], t$95$1, If[LessEqual[a, 6.2e+83], t$95$3, If[LessEqual[a, 6.4e+83], y, t$95$2]]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if a < -3.49999999999999976e100 or 6.3999999999999998e83 < a

   1. Initial program 70.9%

      \[x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \]
   2. Step-by-step derivation

      1. associate-*l/ 89.9%

         \[\leadsto x + \color{blue}{\frac{y - x}{a - t} \cdot \left(z - t\right)} \]

   3. Simplified 89.9%

      \[\leadsto \color{blue}{x + \frac{y - x}{a - t} \cdot \left(z - t\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in t around 0 69.4%

      \[\leadsto \color{blue}{x + \frac{z \cdot \left(y - x\right)}{a}} \]

   6. Taylor expanded in y around inf 68.7%

      \[\leadsto x + \color{blue}{\frac{y \cdot z}{a}} \]
   7. Step-by-step derivation

      1. associate-/l* 76.0%

         \[\leadsto x + \color{blue}{\frac{y}{\frac{a}{z}}} \]

   8. Simplified 76.0%

      \[\leadsto x + \color{blue}{\frac{y}{\frac{a}{z}}} \]

   if -3.49999999999999976e100 < a < -3.6999999999999998e-112 or -2.40000000000000002e-200 < a < 4.79999999999999965e31

   1. Initial program 60.9%

      \[x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \]
   2. Step-by-step derivation

      1. +-commutative 60.9%

         \[\leadsto \color{blue}{\frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} + x} \]

      2. associate-*l/ 67.3%

         \[\leadsto \color{blue}{\frac{y - x}{a - t} \cdot \left(z - t\right)} + x \]

      3. fma-def 67.5%

         \[\leadsto \color{blue}{\mathsf{fma}\left(\frac{y - x}{a - t}, z - t, x\right)} \]

   3. Simplified 67.5%

      \[\leadsto \color{blue}{\mathsf{fma}\left(\frac{y - x}{a - t}, z - t, x\right)} \]
   4. Add Preprocessing
   5. Step-by-step derivation

      1. fma-udef 67.3%

         \[\leadsto \color{blue}{\frac{y - x}{a - t} \cdot \left(z - t\right) + x} \]

      2. associate-/r/ 77.0%

         \[\leadsto \color{blue}{\frac{y - x}{\frac{a - t}{z - t}}} + x \]

      3. div-inv 77.0%

         \[\leadsto \color{blue}{\left(y - x\right) \cdot \frac{1}{\frac{a - t}{z - t}}} + x \]

      4. clear-num 77.0%

         \[\leadsto \left(y - x\right) \cdot \color{blue}{\frac{z - t}{a - t}} + x \]

   6. Applied egg-rr 77.0%

      \[\leadsto \color{blue}{\left(y - x\right) \cdot \frac{z - t}{a - t} + x} \]

   7. Taylor expanded in y around inf 69.4%

      \[\leadsto \color{blue}{y \cdot \left(\frac{z}{a - t} - \frac{t}{a - t}\right)} \]
   8. Step-by-step derivation

      1. div-sub 69.4%

         \[\leadsto y \cdot \color{blue}{\frac{z - t}{a - t}} \]

   9. Simplified 69.4%

      \[\leadsto \color{blue}{y \cdot \frac{z - t}{a - t}} \]

   if -3.6999999999999998e-112 < a < -2.40000000000000002e-200 or 4.79999999999999965e31 < a < 6.19999999999999984e83

   1. Initial program 62.9%

      \[x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \]
   2. Step-by-step derivation

      1. associate-*l/ 57.4%

         \[\leadsto x + \color{blue}{\frac{y - x}{a - t} \cdot \left(z - t\right)} \]

   3. Simplified 57.4%

      \[\leadsto \color{blue}{x + \frac{y - x}{a - t} \cdot \left(z - t\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in z around inf 78.3%

      \[\leadsto \color{blue}{z \cdot \left(\frac{y}{a - t} - \frac{x}{a - t}\right)} \]
   6. Step-by-step derivation

      1. div-sub 78.3%

         \[\leadsto z \cdot \color{blue}{\frac{y - x}{a - t}} \]

   7. Simplified 78.3%

      \[\leadsto \color{blue}{z \cdot \frac{y - x}{a - t}} \]

   if 6.19999999999999984e83 < a < 6.3999999999999998e83

   1. Initial program 9.9%

      \[x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \]
   2. Step-by-step derivation

      1. associate-*l/ 100.0%

         \[\leadsto x + \color{blue}{\frac{y - x}{a - t} \cdot \left(z - t\right)} \]

   3. Simplified 100.0%

      \[\leadsto \color{blue}{x + \frac{y - x}{a - t} \cdot \left(z - t\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in t around inf 100.0%

      \[\leadsto \color{blue}{y} \]
3. Recombined 4 regimes into one program.

4. Final simplification 72.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -3.5 \cdot 10^{+100}:\\ \;\;\;\;x + \frac{y}{\frac{a}{z}}\\ \mathbf{elif}\;a \leq -3.7 \cdot 10^{-112}:\\ \;\;\;\;y \cdot \frac{z - t}{a - t}\\ \mathbf{elif}\;a \leq -2.4 \cdot 10^{-200}:\\ \;\;\;\;z \cdot \frac{y - x}{a - t}\\ \mathbf{elif}\;a \leq 4.8 \cdot 10^{+31}:\\ \;\;\;\;y \cdot \frac{z - t}{a - t}\\ \mathbf{elif}\;a \leq 6.2 \cdot 10^{+83}:\\ \;\;\;\;z \cdot \frac{y - x}{a - t}\\ \mathbf{elif}\;a \leq 6.4 \cdot 10^{+83}:\\ \;\;\;\;y\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{\frac{a}{z}}\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 37.4% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -1.15 \cdot 10^{+92}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq -4 \cdot 10^{+31}:\\ \;\;\;\;y\\ \mathbf{elif}\;a \leq -1.45 \cdot 10^{+18}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq -8.6 \cdot 10^{-72}:\\ \;\;\;\;x \cdot \frac{z - a}{t}\\ \mathbf{elif}\;a \leq -1.7 \cdot 10^{-108}:\\ \;\;\;\;y\\ \mathbf{elif}\;a \leq -2.05 \cdot 10^{-201}:\\ \;\;\;\;\frac{x}{\frac{t}{z}}\\ \mathbf{elif}\;a \leq 6.5 \cdot 10^{+83}:\\ \;\;\;\;y\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= a -1.15e+92)
   x
   (if (<= a -4e+31)
     y
     (if (<= a -1.45e+18)
       x
       (if (<= a -8.6e-72)
         (* x (/ (- z a) t))
         (if (<= a -1.7e-108)
           y
           (if (<= a -2.05e-201) (/ x (/ t z)) (if (<= a 6.5e+83) y x))))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -1.15e+92) {
		tmp = x;
	} else if (a <= -4e+31) {
		tmp = y;
	} else if (a <= -1.45e+18) {
		tmp = x;
	} else if (a <= -8.6e-72) {
		tmp = x * ((z - a) / t);
	} else if (a <= -1.7e-108) {
		tmp = y;
	} else if (a <= -2.05e-201) {
		tmp = x / (t / z);
	} else if (a <= 6.5e+83) {
		tmp = y;
	} else {
		tmp = x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (a <= (-1.15d+92)) then
        tmp = x
    else if (a <= (-4d+31)) then
        tmp = y
    else if (a <= (-1.45d+18)) then
        tmp = x
    else if (a <= (-8.6d-72)) then
        tmp = x * ((z - a) / t)
    else if (a <= (-1.7d-108)) then
        tmp = y
    else if (a <= (-2.05d-201)) then
        tmp = x / (t / z)
    else if (a <= 6.5d+83) then
        tmp = y
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -1.15e+92) {
		tmp = x;
	} else if (a <= -4e+31) {
		tmp = y;
	} else if (a <= -1.45e+18) {
		tmp = x;
	} else if (a <= -8.6e-72) {
		tmp = x * ((z - a) / t);
	} else if (a <= -1.7e-108) {
		tmp = y;
	} else if (a <= -2.05e-201) {
		tmp = x / (t / z);
	} else if (a <= 6.5e+83) {
		tmp = y;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if a <= -1.15e+92:
		tmp = x
	elif a <= -4e+31:
		tmp = y
	elif a <= -1.45e+18:
		tmp = x
	elif a <= -8.6e-72:
		tmp = x * ((z - a) / t)
	elif a <= -1.7e-108:
		tmp = y
	elif a <= -2.05e-201:
		tmp = x / (t / z)
	elif a <= 6.5e+83:
		tmp = y
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (a <= -1.15e+92)
		tmp = x;
	elseif (a <= -4e+31)
		tmp = y;
	elseif (a <= -1.45e+18)
		tmp = x;
	elseif (a <= -8.6e-72)
		tmp = Float64(x * Float64(Float64(z - a) / t));
	elseif (a <= -1.7e-108)
		tmp = y;
	elseif (a <= -2.05e-201)
		tmp = Float64(x / Float64(t / z));
	elseif (a <= 6.5e+83)
		tmp = y;
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (a <= -1.15e+92)
		tmp = x;
	elseif (a <= -4e+31)
		tmp = y;
	elseif (a <= -1.45e+18)
		tmp = x;
	elseif (a <= -8.6e-72)
		tmp = x * ((z - a) / t);
	elseif (a <= -1.7e-108)
		tmp = y;
	elseif (a <= -2.05e-201)
		tmp = x / (t / z);
	elseif (a <= 6.5e+83)
		tmp = y;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[a, -1.15e+92], x, If[LessEqual[a, -4e+31], y, If[LessEqual[a, -1.45e+18], x, If[LessEqual[a, -8.6e-72], N[(x * N[(N[(z - a), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, -1.7e-108], y, If[LessEqual[a, -2.05e-201], N[(x / N[(t / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 6.5e+83], y, x]]]]]]]

Derivation

1. Split input into 4 regimes

2. if a < -1.14999999999999999e92 or -3.9999999999999999e31 < a < -1.45e18 or 6.5000000000000003e83 < a

   1. Initial program 70.7%

      \[x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \]
   2. Step-by-step derivation

      1. associate-*l/ 89.1%

         \[\leadsto x + \color{blue}{\frac{y - x}{a - t} \cdot \left(z - t\right)} \]

   3. Simplified 89.1%

      \[\leadsto \color{blue}{x + \frac{y - x}{a - t} \cdot \left(z - t\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in a around inf 60.4%

      \[\leadsto \color{blue}{x} \]

   if -1.14999999999999999e92 < a < -3.9999999999999999e31 or -8.5999999999999998e-72 < a < -1.70000000000000001e-108 or -2.05000000000000001e-201 < a < 6.5000000000000003e83

   1. Initial program 63.0%

      \[x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \]
   2. Step-by-step derivation

      1. associate-*l/ 69.8%

         \[\leadsto x + \color{blue}{\frac{y - x}{a - t} \cdot \left(z - t\right)} \]

   3. Simplified 69.8%

      \[\leadsto \color{blue}{x + \frac{y - x}{a - t} \cdot \left(z - t\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in t around inf 44.3%

      \[\leadsto \color{blue}{y} \]

   if -1.45e18 < a < -8.5999999999999998e-72

   1. Initial program 51.6%

      \[x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \]
   2. Step-by-step derivation

      1. associate-*l/ 56.9%

         \[\leadsto x + \color{blue}{\frac{y - x}{a - t} \cdot \left(z - t\right)} \]

   3. Simplified 56.9%

      \[\leadsto \color{blue}{x + \frac{y - x}{a - t} \cdot \left(z - t\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in t around inf 52.1%

      \[\leadsto \color{blue}{\left(y + -1 \cdot \frac{z \cdot \left(y - x\right)}{t}\right) - -1 \cdot \frac{a \cdot \left(y - x\right)}{t}} \]
   6. Step-by-step derivation

      1. associate--l+ 52.1%

         \[\leadsto \color{blue}{y + \left(-1 \cdot \frac{z \cdot \left(y - x\right)}{t} - -1 \cdot \frac{a \cdot \left(y - x\right)}{t}\right)} \]

      2. associate-*r/ 52.1%

         \[\leadsto y + \left(\color{blue}{\frac{-1 \cdot \left(z \cdot \left(y - x\right)\right)}{t}} - -1 \cdot \frac{a \cdot \left(y - x\right)}{t}\right) \]

      3. associate-*r/ 52.1%

         \[\leadsto y + \left(\frac{-1 \cdot \left(z \cdot \left(y - x\right)\right)}{t} - \color{blue}{\frac{-1 \cdot \left(a \cdot \left(y - x\right)\right)}{t}}\right) \]

      4. div-sub 52.0%

         \[\leadsto y + \color{blue}{\frac{-1 \cdot \left(z \cdot \left(y - x\right)\right) - -1 \cdot \left(a \cdot \left(y - x\right)\right)}{t}} \]

      5. distribute-lft-out-- 52.0%

         \[\leadsto y + \frac{\color{blue}{-1 \cdot \left(z \cdot \left(y - x\right) - a \cdot \left(y - x\right)\right)}}{t} \]

      6. associate-*r/ 52.0%

         \[\leadsto y + \color{blue}{-1 \cdot \frac{z \cdot \left(y - x\right) - a \cdot \left(y - x\right)}{t}} \]

      7. mul-1-neg 52.0%

         \[\leadsto y + \color{blue}{\left(-\frac{z \cdot \left(y - x\right) - a \cdot \left(y - x\right)}{t}\right)} \]

      8. unsub-neg 52.0%

         \[\leadsto \color{blue}{y - \frac{z \cdot \left(y - x\right) - a \cdot \left(y - x\right)}{t}} \]

      9. distribute-rgt-out-- 52.1%

         \[\leadsto y - \frac{\color{blue}{\left(y - x\right) \cdot \left(z - a\right)}}{t} \]

      10. associate-/l* 67.7%

          \[\leadsto y - \color{blue}{\frac{y - x}{\frac{t}{z - a}}} \]

   7. Simplified 67.7%

      \[\leadsto \color{blue}{y - \frac{y - x}{\frac{t}{z - a}}} \]

   8. Taylor expanded in y around 0 31.2%

      \[\leadsto \color{blue}{\frac{x \cdot \left(z - a\right)}{t}} \]
   9. Step-by-step derivation

      1. associate-*r/ 41.9%

         \[\leadsto \color{blue}{x \cdot \frac{z - a}{t}} \]

   10. Simplified 41.9%

       \[\leadsto \color{blue}{x \cdot \frac{z - a}{t}} \]

   if -1.70000000000000001e-108 < a < -2.05000000000000001e-201

   1. Initial program 55.6%

      \[x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \]
   2. Step-by-step derivation

      1. associate-*l/ 47.4%

         \[\leadsto x + \color{blue}{\frac{y - x}{a - t} \cdot \left(z - t\right)} \]

   3. Simplified 47.4%

      \[\leadsto \color{blue}{x + \frac{y - x}{a - t} \cdot \left(z - t\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in x around -inf 72.7%

      \[\leadsto \color{blue}{-1 \cdot \left(x \cdot \left(\frac{z}{a - t} - \left(1 + \frac{t}{a - t}\right)\right)\right)} \]
   6. Step-by-step derivation

      1. associate-*r* 72.7%

         \[\leadsto \color{blue}{\left(-1 \cdot x\right) \cdot \left(\frac{z}{a - t} - \left(1 + \frac{t}{a - t}\right)\right)} \]

      2. neg-mul-1 72.7%

         \[\leadsto \color{blue}{\left(-x\right)} \cdot \left(\frac{z}{a - t} - \left(1 + \frac{t}{a - t}\right)\right) \]

   7. Simplified 72.7%

      \[\leadsto \color{blue}{\left(-x\right) \cdot \left(\frac{z}{a - t} - \left(1 + \frac{t}{a - t}\right)\right)} \]

   8. Taylor expanded in a around 0 52.9%

      \[\leadsto \color{blue}{\frac{x \cdot z}{t}} \]
   9. Step-by-step derivation

      1. associate-/l* 62.7%

         \[\leadsto \color{blue}{\frac{x}{\frac{t}{z}}} \]

   10. Simplified 62.7%

       \[\leadsto \color{blue}{\frac{x}{\frac{t}{z}}} \]
3. Recombined 4 regimes into one program.

4. Final simplification 51.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -1.15 \cdot 10^{+92}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq -4 \cdot 10^{+31}:\\ \;\;\;\;y\\ \mathbf{elif}\;a \leq -1.45 \cdot 10^{+18}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq -8.6 \cdot 10^{-72}:\\ \;\;\;\;x \cdot \frac{z - a}{t}\\ \mathbf{elif}\;a \leq -1.7 \cdot 10^{-108}:\\ \;\;\;\;y\\ \mathbf{elif}\;a \leq -2.05 \cdot 10^{-201}:\\ \;\;\;\;\frac{x}{\frac{t}{z}}\\ \mathbf{elif}\;a \leq 6.5 \cdot 10^{+83}:\\ \;\;\;\;y\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 50.1% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -1.22 \cdot 10^{+237}:\\ \;\;\;\;y\\ \mathbf{elif}\;t \leq -7 \cdot 10^{+58}:\\ \;\;\;\;\frac{z}{\frac{t}{x - y}}\\ \mathbf{elif}\;t \leq 3.71 \cdot 10^{+90}:\\ \;\;\;\;x + \frac{y}{\frac{a}{z}}\\ \mathbf{elif}\;t \leq 1.95 \cdot 10^{+225}:\\ \;\;\;\;y\\ \mathbf{elif}\;t \leq 2.8 \cdot 10^{+272}:\\ \;\;\;\;x \cdot \frac{z - a}{t}\\ \mathbf{else}:\\ \;\;\;\;y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= t -1.22e+237)
   y
   (if (<= t -7e+58)
     (/ z (/ t (- x y)))
     (if (<= t 3.71e+90)
       (+ x (/ y (/ a z)))
       (if (<= t 1.95e+225) y (if (<= t 2.8e+272) (* x (/ (- z a) t)) y))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= -1.22e+237) {
		tmp = y;
	} else if (t <= -7e+58) {
		tmp = z / (t / (x - y));
	} else if (t <= 3.71e+90) {
		tmp = x + (y / (a / z));
	} else if (t <= 1.95e+225) {
		tmp = y;
	} else if (t <= 2.8e+272) {
		tmp = x * ((z - a) / t);
	} else {
		tmp = y;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (t <= (-1.22d+237)) then
        tmp = y
    else if (t <= (-7d+58)) then
        tmp = z / (t / (x - y))
    else if (t <= 3.71d+90) then
        tmp = x + (y / (a / z))
    else if (t <= 1.95d+225) then
        tmp = y
    else if (t <= 2.8d+272) then
        tmp = x * ((z - a) / t)
    else
        tmp = y
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= -1.22e+237) {
		tmp = y;
	} else if (t <= -7e+58) {
		tmp = z / (t / (x - y));
	} else if (t <= 3.71e+90) {
		tmp = x + (y / (a / z));
	} else if (t <= 1.95e+225) {
		tmp = y;
	} else if (t <= 2.8e+272) {
		tmp = x * ((z - a) / t);
	} else {
		tmp = y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if t <= -1.22e+237:
		tmp = y
	elif t <= -7e+58:
		tmp = z / (t / (x - y))
	elif t <= 3.71e+90:
		tmp = x + (y / (a / z))
	elif t <= 1.95e+225:
		tmp = y
	elif t <= 2.8e+272:
		tmp = x * ((z - a) / t)
	else:
		tmp = y
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (t <= -1.22e+237)
		tmp = y;
	elseif (t <= -7e+58)
		tmp = Float64(z / Float64(t / Float64(x - y)));
	elseif (t <= 3.71e+90)
		tmp = Float64(x + Float64(y / Float64(a / z)));
	elseif (t <= 1.95e+225)
		tmp = y;
	elseif (t <= 2.8e+272)
		tmp = Float64(x * Float64(Float64(z - a) / t));
	else
		tmp = y;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (t <= -1.22e+237)
		tmp = y;
	elseif (t <= -7e+58)
		tmp = z / (t / (x - y));
	elseif (t <= 3.71e+90)
		tmp = x + (y / (a / z));
	elseif (t <= 1.95e+225)
		tmp = y;
	elseif (t <= 2.8e+272)
		tmp = x * ((z - a) / t);
	else
		tmp = y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[t, -1.22e+237], y, If[LessEqual[t, -7e+58], N[(z / N[(t / N[(x - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 3.71e+90], N[(x + N[(y / N[(a / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 1.95e+225], y, If[LessEqual[t, 2.8e+272], N[(x * N[(N[(z - a), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision], y]]]]]

Derivation

1. Split input into 4 regimes

2. if t < -1.2200000000000001e237 or 3.7100000000000001e90 < t < 1.95000000000000012e225 or 2.7999999999999999e272 < t

   1. Initial program 25.9%

      \[x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \]
   2. Step-by-step derivation

      1. associate-*l/ 54.7%

         \[\leadsto x + \color{blue}{\frac{y - x}{a - t} \cdot \left(z - t\right)} \]

   3. Simplified 54.7%

      \[\leadsto \color{blue}{x + \frac{y - x}{a - t} \cdot \left(z - t\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in t around inf 58.2%

      \[\leadsto \color{blue}{y} \]

   if -1.2200000000000001e237 < t < -6.9999999999999995e58

   1. Initial program 55.2%

      \[x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \]
   2. Step-by-step derivation

      1. associate-*l/ 69.8%

         \[\leadsto x + \color{blue}{\frac{y - x}{a - t} \cdot \left(z - t\right)} \]

   3. Simplified 69.8%

      \[\leadsto \color{blue}{x + \frac{y - x}{a - t} \cdot \left(z - t\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in t around inf 58.1%

      \[\leadsto \color{blue}{\left(y + -1 \cdot \frac{z \cdot \left(y - x\right)}{t}\right) - -1 \cdot \frac{a \cdot \left(y - x\right)}{t}} \]
   6. Step-by-step derivation

      1. associate--l+ 58.1%

         \[\leadsto \color{blue}{y + \left(-1 \cdot \frac{z \cdot \left(y - x\right)}{t} - -1 \cdot \frac{a \cdot \left(y - x\right)}{t}\right)} \]

      2. associate-*r/ 58.1%

         \[\leadsto y + \left(\color{blue}{\frac{-1 \cdot \left(z \cdot \left(y - x\right)\right)}{t}} - -1 \cdot \frac{a \cdot \left(y - x\right)}{t}\right) \]

      3. associate-*r/ 58.1%

         \[\leadsto y + \left(\frac{-1 \cdot \left(z \cdot \left(y - x\right)\right)}{t} - \color{blue}{\frac{-1 \cdot \left(a \cdot \left(y - x\right)\right)}{t}}\right) \]

      4. div-sub 58.2%

         \[\leadsto y + \color{blue}{\frac{-1 \cdot \left(z \cdot \left(y - x\right)\right) - -1 \cdot \left(a \cdot \left(y - x\right)\right)}{t}} \]

      5. distribute-lft-out-- 58.2%

         \[\leadsto y + \frac{\color{blue}{-1 \cdot \left(z \cdot \left(y - x\right) - a \cdot \left(y - x\right)\right)}}{t} \]

      6. associate-*r/ 58.2%

         \[\leadsto y + \color{blue}{-1 \cdot \frac{z \cdot \left(y - x\right) - a \cdot \left(y - x\right)}{t}} \]

      7. mul-1-neg 58.2%

         \[\leadsto y + \color{blue}{\left(-\frac{z \cdot \left(y - x\right) - a \cdot \left(y - x\right)}{t}\right)} \]

      8. unsub-neg 58.2%

         \[\leadsto \color{blue}{y - \frac{z \cdot \left(y - x\right) - a \cdot \left(y - x\right)}{t}} \]

      9. distribute-rgt-out-- 58.2%

         \[\leadsto y - \frac{\color{blue}{\left(y - x\right) \cdot \left(z - a\right)}}{t} \]

      10. associate-/l* 74.0%

          \[\leadsto y - \color{blue}{\frac{y - x}{\frac{t}{z - a}}} \]

   7. Simplified 74.0%

      \[\leadsto \color{blue}{y - \frac{y - x}{\frac{t}{z - a}}} \]

   8. Taylor expanded in z around -inf 38.4%

      \[\leadsto \color{blue}{-1 \cdot \frac{z \cdot \left(y - x\right)}{t}} \]
   9. Step-by-step derivation

      1. associate-*r/ 38.4%

         \[\leadsto \color{blue}{\frac{-1 \cdot \left(z \cdot \left(y - x\right)\right)}{t}} \]

      2. mul-1-neg 38.4%

         \[\leadsto \frac{\color{blue}{-z \cdot \left(y - x\right)}}{t} \]

   10. Simplified 38.4%

       \[\leadsto \color{blue}{\frac{-z \cdot \left(y - x\right)}{t}} \]

   11. Taylor expanded in z around inf 38.4%

       \[\leadsto \color{blue}{\frac{z \cdot \left(x - y\right)}{t}} \]
   12. Step-by-step derivation

       1. associate-/l* 51.5%

          \[\leadsto \color{blue}{\frac{z}{\frac{t}{x - y}}} \]

   13. Simplified 51.5%

       \[\leadsto \color{blue}{\frac{z}{\frac{t}{x - y}}} \]

   if -6.9999999999999995e58 < t < 3.7100000000000001e90

   1. Initial program 85.4%

      \[x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \]
   2. Step-by-step derivation

      1. associate-*l/ 85.8%

         \[\leadsto x + \color{blue}{\frac{y - x}{a - t} \cdot \left(z - t\right)} \]

   3. Simplified 85.8%

      \[\leadsto \color{blue}{x + \frac{y - x}{a - t} \cdot \left(z - t\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in t around 0 62.6%

      \[\leadsto \color{blue}{x + \frac{z \cdot \left(y - x\right)}{a}} \]

   6. Taylor expanded in y around inf 55.4%

      \[\leadsto x + \color{blue}{\frac{y \cdot z}{a}} \]
   7. Step-by-step derivation

      1. associate-/l* 59.0%

         \[\leadsto x + \color{blue}{\frac{y}{\frac{a}{z}}} \]

   8. Simplified 59.0%

      \[\leadsto x + \color{blue}{\frac{y}{\frac{a}{z}}} \]

   if 1.95000000000000012e225 < t < 2.7999999999999999e272

   1. Initial program 11.0%

      \[x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \]
   2. Step-by-step derivation

      1. associate-*l/ 37.6%

         \[\leadsto x + \color{blue}{\frac{y - x}{a - t} \cdot \left(z - t\right)} \]

   3. Simplified 37.6%

      \[\leadsto \color{blue}{x + \frac{y - x}{a - t} \cdot \left(z - t\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in t around inf 55.9%

      \[\leadsto \color{blue}{\left(y + -1 \cdot \frac{z \cdot \left(y - x\right)}{t}\right) - -1 \cdot \frac{a \cdot \left(y - x\right)}{t}} \]
   6. Step-by-step derivation

      1. associate--l+ 55.9%

         \[\leadsto \color{blue}{y + \left(-1 \cdot \frac{z \cdot \left(y - x\right)}{t} - -1 \cdot \frac{a \cdot \left(y - x\right)}{t}\right)} \]

      2. associate-*r/ 55.9%

         \[\leadsto y + \left(\color{blue}{\frac{-1 \cdot \left(z \cdot \left(y - x\right)\right)}{t}} - -1 \cdot \frac{a \cdot \left(y - x\right)}{t}\right) \]

      3. associate-*r/ 55.9%

         \[\leadsto y + \left(\frac{-1 \cdot \left(z \cdot \left(y - x\right)\right)}{t} - \color{blue}{\frac{-1 \cdot \left(a \cdot \left(y - x\right)\right)}{t}}\right) \]

      4. div-sub 55.9%

         \[\leadsto y + \color{blue}{\frac{-1 \cdot \left(z \cdot \left(y - x\right)\right) - -1 \cdot \left(a \cdot \left(y - x\right)\right)}{t}} \]

      5. distribute-lft-out-- 55.9%

         \[\leadsto y + \frac{\color{blue}{-1 \cdot \left(z \cdot \left(y - x\right) - a \cdot \left(y - x\right)\right)}}{t} \]

      6. associate-*r/ 55.9%

         \[\leadsto y + \color{blue}{-1 \cdot \frac{z \cdot \left(y - x\right) - a \cdot \left(y - x\right)}{t}} \]

      7. mul-1-neg 55.9%

         \[\leadsto y + \color{blue}{\left(-\frac{z \cdot \left(y - x\right) - a \cdot \left(y - x\right)}{t}\right)} \]

      8. unsub-neg 55.9%

         \[\leadsto \color{blue}{y - \frac{z \cdot \left(y - x\right) - a \cdot \left(y - x\right)}{t}} \]

      9. distribute-rgt-out-- 55.9%

         \[\leadsto y - \frac{\color{blue}{\left(y - x\right) \cdot \left(z - a\right)}}{t} \]

      10. associate-/l* 92.1%

          \[\leadsto y - \color{blue}{\frac{y - x}{\frac{t}{z - a}}} \]

   7. Simplified 92.1%

      \[\leadsto \color{blue}{y - \frac{y - x}{\frac{t}{z - a}}} \]

   8. Taylor expanded in y around 0 33.7%

      \[\leadsto \color{blue}{\frac{x \cdot \left(z - a\right)}{t}} \]
   9. Step-by-step derivation

      1. associate-*r/ 62.9%

         \[\leadsto \color{blue}{x \cdot \frac{z - a}{t}} \]

   10. Simplified 62.9%

       \[\leadsto \color{blue}{x \cdot \frac{z - a}{t}} \]
3. Recombined 4 regimes into one program.

4. Final simplification 58.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.22 \cdot 10^{+237}:\\ \;\;\;\;y\\ \mathbf{elif}\;t \leq -7 \cdot 10^{+58}:\\ \;\;\;\;\frac{z}{\frac{t}{x - y}}\\ \mathbf{elif}\;t \leq 3.71 \cdot 10^{+90}:\\ \;\;\;\;x + \frac{y}{\frac{a}{z}}\\ \mathbf{elif}\;t \leq 1.95 \cdot 10^{+225}:\\ \;\;\;\;y\\ \mathbf{elif}\;t \leq 2.8 \cdot 10^{+272}:\\ \;\;\;\;x \cdot \frac{z - a}{t}\\ \mathbf{else}:\\ \;\;\;\;y\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 59.7% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y \cdot \frac{z - t}{a - t}\\ t_2 := x + \frac{y}{\frac{a}{z}}\\ \mathbf{if}\;a \leq -5.2 \cdot 10^{+99}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;a \leq -3.2 \cdot 10^{-112}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq -8.4 \cdot 10^{-203}:\\ \;\;\;\;\frac{z}{\frac{t}{x - y}}\\ \mathbf{elif}\;a \leq 6.8 \cdot 10^{+65}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* y (/ (- z t) (- a t)))) (t_2 (+ x (/ y (/ a z)))))
   (if (<= a -5.2e+99)
     t_2
     (if (<= a -3.2e-112)
       t_1
       (if (<= a -8.4e-203)
         (/ z (/ t (- x y)))
         (if (<= a 6.8e+65) t_1 t_2))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = y * ((z - t) / (a - t));
	double t_2 = x + (y / (a / z));
	double tmp;
	if (a <= -5.2e+99) {
		tmp = t_2;
	} else if (a <= -3.2e-112) {
		tmp = t_1;
	} else if (a <= -8.4e-203) {
		tmp = z / (t / (x - y));
	} else if (a <= 6.8e+65) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = y * ((z - t) / (a - t))
    t_2 = x + (y / (a / z))
    if (a <= (-5.2d+99)) then
        tmp = t_2
    else if (a <= (-3.2d-112)) then
        tmp = t_1
    else if (a <= (-8.4d-203)) then
        tmp = z / (t / (x - y))
    else if (a <= 6.8d+65) then
        tmp = t_1
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = y * ((z - t) / (a - t));
	double t_2 = x + (y / (a / z));
	double tmp;
	if (a <= -5.2e+99) {
		tmp = t_2;
	} else if (a <= -3.2e-112) {
		tmp = t_1;
	} else if (a <= -8.4e-203) {
		tmp = z / (t / (x - y));
	} else if (a <= 6.8e+65) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = y * ((z - t) / (a - t))
	t_2 = x + (y / (a / z))
	tmp = 0
	if a <= -5.2e+99:
		tmp = t_2
	elif a <= -3.2e-112:
		tmp = t_1
	elif a <= -8.4e-203:
		tmp = z / (t / (x - y))
	elif a <= 6.8e+65:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(y * Float64(Float64(z - t) / Float64(a - t)))
	t_2 = Float64(x + Float64(y / Float64(a / z)))
	tmp = 0.0
	if (a <= -5.2e+99)
		tmp = t_2;
	elseif (a <= -3.2e-112)
		tmp = t_1;
	elseif (a <= -8.4e-203)
		tmp = Float64(z / Float64(t / Float64(x - y)));
	elseif (a <= 6.8e+65)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = y * ((z - t) / (a - t));
	t_2 = x + (y / (a / z));
	tmp = 0.0;
	if (a <= -5.2e+99)
		tmp = t_2;
	elseif (a <= -3.2e-112)
		tmp = t_1;
	elseif (a <= -8.4e-203)
		tmp = z / (t / (x - y));
	elseif (a <= 6.8e+65)
		tmp = t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(y * N[(N[(z - t), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x + N[(y / N[(a / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -5.2e+99], t$95$2, If[LessEqual[a, -3.2e-112], t$95$1, If[LessEqual[a, -8.4e-203], N[(z / N[(t / N[(x - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 6.8e+65], t$95$1, t$95$2]]]]]]

Derivation

1. Split input into 3 regimes

2. if a < -5.1999999999999999e99 or 6.7999999999999999e65 < a

   1. Initial program 71.1%

      \[x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \]
   2. Step-by-step derivation

      1. associate-*l/ 90.3%

         \[\leadsto x + \color{blue}{\frac{y - x}{a - t} \cdot \left(z - t\right)} \]

   3. Simplified 90.3%

      \[\leadsto \color{blue}{x + \frac{y - x}{a - t} \cdot \left(z - t\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in t around 0 69.7%

      \[\leadsto \color{blue}{x + \frac{z \cdot \left(y - x\right)}{a}} \]

   6. Taylor expanded in y around inf 69.0%

      \[\leadsto x + \color{blue}{\frac{y \cdot z}{a}} \]
   7. Step-by-step derivation

      1. associate-/l* 75.0%

         \[\leadsto x + \color{blue}{\frac{y}{\frac{a}{z}}} \]

   8. Simplified 75.0%

      \[\leadsto x + \color{blue}{\frac{y}{\frac{a}{z}}} \]

   if -5.1999999999999999e99 < a < -3.19999999999999993e-112 or -8.40000000000000008e-203 < a < 6.7999999999999999e65

   1. Initial program 61.2%

      \[x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \]
   2. Step-by-step derivation

      1. +-commutative 61.2%

         \[\leadsto \color{blue}{\frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} + x} \]

      2. associate-*l/ 67.3%

         \[\leadsto \color{blue}{\frac{y - x}{a - t} \cdot \left(z - t\right)} + x \]

      3. fma-def 67.6%

         \[\leadsto \color{blue}{\mathsf{fma}\left(\frac{y - x}{a - t}, z - t, x\right)} \]

   3. Simplified 67.6%

      \[\leadsto \color{blue}{\mathsf{fma}\left(\frac{y - x}{a - t}, z - t, x\right)} \]
   4. Add Preprocessing
   5. Step-by-step derivation

      1. fma-udef 67.3%

         \[\leadsto \color{blue}{\frac{y - x}{a - t} \cdot \left(z - t\right) + x} \]

      2. associate-/r/ 76.7%

         \[\leadsto \color{blue}{\frac{y - x}{\frac{a - t}{z - t}}} + x \]

      3. div-inv 76.6%

         \[\leadsto \color{blue}{\left(y - x\right) \cdot \frac{1}{\frac{a - t}{z - t}}} + x \]

      4. clear-num 76.6%

         \[\leadsto \left(y - x\right) \cdot \color{blue}{\frac{z - t}{a - t}} + x \]

   6. Applied egg-rr 76.6%

      \[\leadsto \color{blue}{\left(y - x\right) \cdot \frac{z - t}{a - t} + x} \]

   7. Taylor expanded in y around inf 67.3%

      \[\leadsto \color{blue}{y \cdot \left(\frac{z}{a - t} - \frac{t}{a - t}\right)} \]
   8. Step-by-step derivation

      1. div-sub 67.3%

         \[\leadsto y \cdot \color{blue}{\frac{z - t}{a - t}} \]

   9. Simplified 67.3%

      \[\leadsto \color{blue}{y \cdot \frac{z - t}{a - t}} \]

   if -3.19999999999999993e-112 < a < -8.40000000000000008e-203

   1. Initial program 55.6%

      \[x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \]
   2. Step-by-step derivation

      1. associate-*l/ 47.4%

         \[\leadsto x + \color{blue}{\frac{y - x}{a - t} \cdot \left(z - t\right)} \]

   3. Simplified 47.4%

      \[\leadsto \color{blue}{x + \frac{y - x}{a - t} \cdot \left(z - t\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in t around inf 69.9%

      \[\leadsto \color{blue}{\left(y + -1 \cdot \frac{z \cdot \left(y - x\right)}{t}\right) - -1 \cdot \frac{a \cdot \left(y - x\right)}{t}} \]
   6. Step-by-step derivation

      1. associate--l+ 69.9%

         \[\leadsto \color{blue}{y + \left(-1 \cdot \frac{z \cdot \left(y - x\right)}{t} - -1 \cdot \frac{a \cdot \left(y - x\right)}{t}\right)} \]

      2. associate-*r/ 69.9%

         \[\leadsto y + \left(\color{blue}{\frac{-1 \cdot \left(z \cdot \left(y - x\right)\right)}{t}} - -1 \cdot \frac{a \cdot \left(y - x\right)}{t}\right) \]

      3. associate-*r/ 69.9%

         \[\leadsto y + \left(\frac{-1 \cdot \left(z \cdot \left(y - x\right)\right)}{t} - \color{blue}{\frac{-1 \cdot \left(a \cdot \left(y - x\right)\right)}{t}}\right) \]

      4. div-sub 69.9%

         \[\leadsto y + \color{blue}{\frac{-1 \cdot \left(z \cdot \left(y - x\right)\right) - -1 \cdot \left(a \cdot \left(y - x\right)\right)}{t}} \]

      5. distribute-lft-out-- 69.9%

         \[\leadsto y + \frac{\color{blue}{-1 \cdot \left(z \cdot \left(y - x\right) - a \cdot \left(y - x\right)\right)}}{t} \]

      6. associate-*r/ 69.9%

         \[\leadsto y + \color{blue}{-1 \cdot \frac{z \cdot \left(y - x\right) - a \cdot \left(y - x\right)}{t}} \]

      7. mul-1-neg 69.9%

         \[\leadsto y + \color{blue}{\left(-\frac{z \cdot \left(y - x\right) - a \cdot \left(y - x\right)}{t}\right)} \]

      8. unsub-neg 69.9%

         \[\leadsto \color{blue}{y - \frac{z \cdot \left(y - x\right) - a \cdot \left(y - x\right)}{t}} \]

      9. distribute-rgt-out-- 69.9%

         \[\leadsto y - \frac{\color{blue}{\left(y - x\right) \cdot \left(z - a\right)}}{t} \]

      10. associate-/l* 84.4%

          \[\leadsto y - \color{blue}{\frac{y - x}{\frac{t}{z - a}}} \]

   7. Simplified 84.4%

      \[\leadsto \color{blue}{y - \frac{y - x}{\frac{t}{z - a}}} \]

   8. Taylor expanded in z around -inf 68.2%

      \[\leadsto \color{blue}{-1 \cdot \frac{z \cdot \left(y - x\right)}{t}} \]
   9. Step-by-step derivation

      1. associate-*r/ 68.2%

         \[\leadsto \color{blue}{\frac{-1 \cdot \left(z \cdot \left(y - x\right)\right)}{t}} \]

      2. mul-1-neg 68.2%

         \[\leadsto \frac{\color{blue}{-z \cdot \left(y - x\right)}}{t} \]

   10. Simplified 68.2%

       \[\leadsto \color{blue}{\frac{-z \cdot \left(y - x\right)}{t}} \]

   11. Taylor expanded in z around inf 68.2%

       \[\leadsto \color{blue}{\frac{z \cdot \left(x - y\right)}{t}} \]
   12. Step-by-step derivation

       1. associate-/l* 72.9%

          \[\leadsto \color{blue}{\frac{z}{\frac{t}{x - y}}} \]

   13. Simplified 72.9%

       \[\leadsto \color{blue}{\frac{z}{\frac{t}{x - y}}} \]
3. Recombined 3 regimes into one program.

4. Final simplification 70.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -5.2 \cdot 10^{+99}:\\ \;\;\;\;x + \frac{y}{\frac{a}{z}}\\ \mathbf{elif}\;a \leq -3.2 \cdot 10^{-112}:\\ \;\;\;\;y \cdot \frac{z - t}{a - t}\\ \mathbf{elif}\;a \leq -8.4 \cdot 10^{-203}:\\ \;\;\;\;\frac{z}{\frac{t}{x - y}}\\ \mathbf{elif}\;a \leq 6.8 \cdot 10^{+65}:\\ \;\;\;\;y \cdot \frac{z - t}{a - t}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{\frac{a}{z}}\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 63.6% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := y \cdot \frac{z - t}{a - t}\\ \mathbf{if}\;a \leq -3.2 \cdot 10^{+92}:\\ \;\;\;\;x - \frac{y}{a} \cdot \left(t - z\right)\\ \mathbf{elif}\;a \leq -5.2 \cdot 10^{-108}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq -1.1 \cdot 10^{-199}:\\ \;\;\;\;z \cdot \frac{y - x}{a - t}\\ \mathbf{elif}\;a \leq 4.9 \cdot 10^{+44}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;x + \frac{z}{\frac{a}{y - x}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* y (/ (- z t) (- a t)))))
   (if (<= a -3.2e+92)
     (- x (* (/ y a) (- t z)))
     (if (<= a -5.2e-108)
       t_1
       (if (<= a -1.1e-199)
         (* z (/ (- y x) (- a t)))
         (if (<= a 4.9e+44) t_1 (+ x (/ z (/ a (- y x))))))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = y * ((z - t) / (a - t));
	double tmp;
	if (a <= -3.2e+92) {
		tmp = x - ((y / a) * (t - z));
	} else if (a <= -5.2e-108) {
		tmp = t_1;
	} else if (a <= -1.1e-199) {
		tmp = z * ((y - x) / (a - t));
	} else if (a <= 4.9e+44) {
		tmp = t_1;
	} else {
		tmp = x + (z / (a / (y - x)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = y * ((z - t) / (a - t))
    if (a <= (-3.2d+92)) then
        tmp = x - ((y / a) * (t - z))
    else if (a <= (-5.2d-108)) then
        tmp = t_1
    else if (a <= (-1.1d-199)) then
        tmp = z * ((y - x) / (a - t))
    else if (a <= 4.9d+44) then
        tmp = t_1
    else
        tmp = x + (z / (a / (y - x)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = y * ((z - t) / (a - t));
	double tmp;
	if (a <= -3.2e+92) {
		tmp = x - ((y / a) * (t - z));
	} else if (a <= -5.2e-108) {
		tmp = t_1;
	} else if (a <= -1.1e-199) {
		tmp = z * ((y - x) / (a - t));
	} else if (a <= 4.9e+44) {
		tmp = t_1;
	} else {
		tmp = x + (z / (a / (y - x)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = y * ((z - t) / (a - t))
	tmp = 0
	if a <= -3.2e+92:
		tmp = x - ((y / a) * (t - z))
	elif a <= -5.2e-108:
		tmp = t_1
	elif a <= -1.1e-199:
		tmp = z * ((y - x) / (a - t))
	elif a <= 4.9e+44:
		tmp = t_1
	else:
		tmp = x + (z / (a / (y - x)))
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(y * Float64(Float64(z - t) / Float64(a - t)))
	tmp = 0.0
	if (a <= -3.2e+92)
		tmp = Float64(x - Float64(Float64(y / a) * Float64(t - z)));
	elseif (a <= -5.2e-108)
		tmp = t_1;
	elseif (a <= -1.1e-199)
		tmp = Float64(z * Float64(Float64(y - x) / Float64(a - t)));
	elseif (a <= 4.9e+44)
		tmp = t_1;
	else
		tmp = Float64(x + Float64(z / Float64(a / Float64(y - x))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = y * ((z - t) / (a - t));
	tmp = 0.0;
	if (a <= -3.2e+92)
		tmp = x - ((y / a) * (t - z));
	elseif (a <= -5.2e-108)
		tmp = t_1;
	elseif (a <= -1.1e-199)
		tmp = z * ((y - x) / (a - t));
	elseif (a <= 4.9e+44)
		tmp = t_1;
	else
		tmp = x + (z / (a / (y - x)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(y * N[(N[(z - t), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -3.2e+92], N[(x - N[(N[(y / a), $MachinePrecision] * N[(t - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, -5.2e-108], t$95$1, If[LessEqual[a, -1.1e-199], N[(z * N[(N[(y - x), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 4.9e+44], t$95$1, N[(x + N[(z / N[(a / N[(y - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 4 regimes

2. if a < -3.20000000000000025e92

   1. Initial program 77.9%

      \[x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \]
   2. Step-by-step derivation

      1. associate-*l/ 89.1%

         \[\leadsto x + \color{blue}{\frac{y - x}{a - t} \cdot \left(z - t\right)} \]

   3. Simplified 89.1%

      \[\leadsto \color{blue}{x + \frac{y - x}{a - t} \cdot \left(z - t\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in a around inf 72.8%

      \[\leadsto \color{blue}{x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a}} \]
   6. Step-by-step derivation

      1. associate-/l* 87.3%

         \[\leadsto x + \color{blue}{\frac{y - x}{\frac{a}{z - t}}} \]

   7. Simplified 87.3%

      \[\leadsto \color{blue}{x + \frac{y - x}{\frac{a}{z - t}}} \]

   8. Taylor expanded in y around inf 72.8%

      \[\leadsto x + \color{blue}{\frac{y \cdot \left(z - t\right)}{a}} \]
   9. Step-by-step derivation

      1. associate-/l* 80.7%

         \[\leadsto x + \color{blue}{\frac{y}{\frac{a}{z - t}}} \]

      2. associate-/r/ 73.8%

         \[\leadsto x + \color{blue}{\frac{y}{a} \cdot \left(z - t\right)} \]

   10. Simplified 73.8%

       \[\leadsto x + \color{blue}{\frac{y}{a} \cdot \left(z - t\right)} \]

   if -3.20000000000000025e92 < a < -5.19999999999999968e-108 or -1.0999999999999999e-199 < a < 4.90000000000000035e44

   1. Initial program 60.3%

      \[x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \]
   2. Step-by-step derivation

      1. +-commutative 60.3%

         \[\leadsto \color{blue}{\frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} + x} \]

      2. associate-*l/ 66.6%

         \[\leadsto \color{blue}{\frac{y - x}{a - t} \cdot \left(z - t\right)} + x \]

      3. fma-def 66.9%

         \[\leadsto \color{blue}{\mathsf{fma}\left(\frac{y - x}{a - t}, z - t, x\right)} \]

   3. Simplified 66.9%

      \[\leadsto \color{blue}{\mathsf{fma}\left(\frac{y - x}{a - t}, z - t, x\right)} \]
   4. Add Preprocessing
   5. Step-by-step derivation

      1. fma-udef 66.6%

         \[\leadsto \color{blue}{\frac{y - x}{a - t} \cdot \left(z - t\right) + x} \]

      2. associate-/r/ 76.4%

         \[\leadsto \color{blue}{\frac{y - x}{\frac{a - t}{z - t}}} + x \]

      3. div-inv 76.3%

         \[\leadsto \color{blue}{\left(y - x\right) \cdot \frac{1}{\frac{a - t}{z - t}}} + x \]

      4. clear-num 76.3%

         \[\leadsto \left(y - x\right) \cdot \color{blue}{\frac{z - t}{a - t}} + x \]

   6. Applied egg-rr 76.3%

      \[\leadsto \color{blue}{\left(y - x\right) \cdot \frac{z - t}{a - t} + x} \]

   7. Taylor expanded in y around inf 68.7%

      \[\leadsto \color{blue}{y \cdot \left(\frac{z}{a - t} - \frac{t}{a - t}\right)} \]
   8. Step-by-step derivation

      1. div-sub 68.7%

         \[\leadsto y \cdot \color{blue}{\frac{z - t}{a - t}} \]

   9. Simplified 68.7%

      \[\leadsto \color{blue}{y \cdot \frac{z - t}{a - t}} \]

   if -5.19999999999999968e-108 < a < -1.0999999999999999e-199

   1. Initial program 55.6%

      \[x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \]
   2. Step-by-step derivation

      1. associate-*l/ 47.4%

         \[\leadsto x + \color{blue}{\frac{y - x}{a - t} \cdot \left(z - t\right)} \]

   3. Simplified 47.4%

      \[\leadsto \color{blue}{x + \frac{y - x}{a - t} \cdot \left(z - t\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in z around inf 78.4%

      \[\leadsto \color{blue}{z \cdot \left(\frac{y}{a - t} - \frac{x}{a - t}\right)} \]
   6. Step-by-step derivation

      1. div-sub 78.4%

         \[\leadsto z \cdot \color{blue}{\frac{y - x}{a - t}} \]

   7. Simplified 78.4%

      \[\leadsto \color{blue}{z \cdot \frac{y - x}{a - t}} \]

   if 4.90000000000000035e44 < a

   1. Initial program 67.4%

      \[x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \]
   2. Step-by-step derivation

      1. associate-*l/ 90.5%

         \[\leadsto x + \color{blue}{\frac{y - x}{a - t} \cdot \left(z - t\right)} \]

   3. Simplified 90.5%

      \[\leadsto \color{blue}{x + \frac{y - x}{a - t} \cdot \left(z - t\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in t around 0 69.8%

      \[\leadsto \color{blue}{x + \frac{z \cdot \left(y - x\right)}{a}} \]
   6. Step-by-step derivation

      1. associate-/l* 83.2%

         \[\leadsto x + \color{blue}{\frac{z}{\frac{a}{y - x}}} \]

   7. Simplified 83.2%

      \[\leadsto \color{blue}{x + \frac{z}{\frac{a}{y - x}}} \]
3. Recombined 4 regimes into one program.

4. Final simplification 73.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -3.2 \cdot 10^{+92}:\\ \;\;\;\;x - \frac{y}{a} \cdot \left(t - z\right)\\ \mathbf{elif}\;a \leq -5.2 \cdot 10^{-108}:\\ \;\;\;\;y \cdot \frac{z - t}{a - t}\\ \mathbf{elif}\;a \leq -1.1 \cdot 10^{-199}:\\ \;\;\;\;z \cdot \frac{y - x}{a - t}\\ \mathbf{elif}\;a \leq 4.9 \cdot 10^{+44}:\\ \;\;\;\;y \cdot \frac{z - t}{a - t}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{z}{\frac{a}{y - x}}\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 54.7% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{-y}{\frac{t}{z - t}}\\ t_2 := x + \frac{y}{\frac{a}{z}}\\ \mathbf{if}\;a \leq -9 \cdot 10^{+50}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;a \leq -6.4 \cdot 10^{-112}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq -2.6 \cdot 10^{-199}:\\ \;\;\;\;\frac{z}{\frac{t}{x - y}}\\ \mathbf{elif}\;a \leq 9 \cdot 10^{+30}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (/ (- y) (/ t (- z t)))) (t_2 (+ x (/ y (/ a z)))))
   (if (<= a -9e+50)
     t_2
     (if (<= a -6.4e-112)
       t_1
       (if (<= a -2.6e-199) (/ z (/ t (- x y))) (if (<= a 9e+30) t_1 t_2))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = -y / (t / (z - t));
	double t_2 = x + (y / (a / z));
	double tmp;
	if (a <= -9e+50) {
		tmp = t_2;
	} else if (a <= -6.4e-112) {
		tmp = t_1;
	} else if (a <= -2.6e-199) {
		tmp = z / (t / (x - y));
	} else if (a <= 9e+30) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = -y / (t / (z - t))
    t_2 = x + (y / (a / z))
    if (a <= (-9d+50)) then
        tmp = t_2
    else if (a <= (-6.4d-112)) then
        tmp = t_1
    else if (a <= (-2.6d-199)) then
        tmp = z / (t / (x - y))
    else if (a <= 9d+30) then
        tmp = t_1
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = -y / (t / (z - t));
	double t_2 = x + (y / (a / z));
	double tmp;
	if (a <= -9e+50) {
		tmp = t_2;
	} else if (a <= -6.4e-112) {
		tmp = t_1;
	} else if (a <= -2.6e-199) {
		tmp = z / (t / (x - y));
	} else if (a <= 9e+30) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = -y / (t / (z - t))
	t_2 = x + (y / (a / z))
	tmp = 0
	if a <= -9e+50:
		tmp = t_2
	elif a <= -6.4e-112:
		tmp = t_1
	elif a <= -2.6e-199:
		tmp = z / (t / (x - y))
	elif a <= 9e+30:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(Float64(-y) / Float64(t / Float64(z - t)))
	t_2 = Float64(x + Float64(y / Float64(a / z)))
	tmp = 0.0
	if (a <= -9e+50)
		tmp = t_2;
	elseif (a <= -6.4e-112)
		tmp = t_1;
	elseif (a <= -2.6e-199)
		tmp = Float64(z / Float64(t / Float64(x - y)));
	elseif (a <= 9e+30)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = -y / (t / (z - t));
	t_2 = x + (y / (a / z));
	tmp = 0.0;
	if (a <= -9e+50)
		tmp = t_2;
	elseif (a <= -6.4e-112)
		tmp = t_1;
	elseif (a <= -2.6e-199)
		tmp = z / (t / (x - y));
	elseif (a <= 9e+30)
		tmp = t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[((-y) / N[(t / N[(z - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x + N[(y / N[(a / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -9e+50], t$95$2, If[LessEqual[a, -6.4e-112], t$95$1, If[LessEqual[a, -2.6e-199], N[(z / N[(t / N[(x - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 9e+30], t$95$1, t$95$2]]]]]]

Derivation

1. Split input into 3 regimes

2. if a < -9.00000000000000027e50 or 8.9999999999999999e30 < a

   1. Initial program 69.6%

      \[x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \]
   2. Step-by-step derivation

      1. associate-*l/ 87.2%

         \[\leadsto x + \color{blue}{\frac{y - x}{a - t} \cdot \left(z - t\right)} \]

   3. Simplified 87.2%

      \[\leadsto \color{blue}{x + \frac{y - x}{a - t} \cdot \left(z - t\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in t around 0 66.6%

      \[\leadsto \color{blue}{x + \frac{z \cdot \left(y - x\right)}{a}} \]

   6. Taylor expanded in y around inf 63.4%

      \[\leadsto x + \color{blue}{\frac{y \cdot z}{a}} \]
   7. Step-by-step derivation

      1. associate-/l* 69.4%

         \[\leadsto x + \color{blue}{\frac{y}{\frac{a}{z}}} \]

   8. Simplified 69.4%

      \[\leadsto x + \color{blue}{\frac{y}{\frac{a}{z}}} \]

   if -9.00000000000000027e50 < a < -6.39999999999999986e-112 or -2.6000000000000001e-199 < a < 8.9999999999999999e30

   1. Initial program 61.5%

      \[x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \]
   2. Step-by-step derivation

      1. +-commutative 61.5%

         \[\leadsto \color{blue}{\frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} + x} \]

      2. associate-*l/ 67.5%

         \[\leadsto \color{blue}{\frac{y - x}{a - t} \cdot \left(z - t\right)} + x \]

      3. fma-def 67.7%

         \[\leadsto \color{blue}{\mathsf{fma}\left(\frac{y - x}{a - t}, z - t, x\right)} \]

   3. Simplified 67.7%

      \[\leadsto \color{blue}{\mathsf{fma}\left(\frac{y - x}{a - t}, z - t, x\right)} \]
   4. Add Preprocessing
   5. Step-by-step derivation

      1. fma-udef 67.5%

         \[\leadsto \color{blue}{\frac{y - x}{a - t} \cdot \left(z - t\right) + x} \]

      2. associate-/r/ 77.1%

         \[\leadsto \color{blue}{\frac{y - x}{\frac{a - t}{z - t}}} + x \]

      3. div-inv 77.1%

         \[\leadsto \color{blue}{\left(y - x\right) \cdot \frac{1}{\frac{a - t}{z - t}}} + x \]

      4. clear-num 77.1%

         \[\leadsto \left(y - x\right) \cdot \color{blue}{\frac{z - t}{a - t}} + x \]

   6. Applied egg-rr 77.1%

      \[\leadsto \color{blue}{\left(y - x\right) \cdot \frac{z - t}{a - t} + x} \]

   7. Taylor expanded in y around -inf 55.5%

      \[\leadsto \color{blue}{\frac{y \cdot \left(z - t\right)}{a - t}} \]
   8. Step-by-step derivation

      1. *-commutative 55.5%

         \[\leadsto \frac{\color{blue}{\left(z - t\right) \cdot y}}{a - t} \]

   9. Simplified 55.5%

      \[\leadsto \color{blue}{\frac{\left(z - t\right) \cdot y}{a - t}} \]

   10. Taylor expanded in a around 0 47.5%

       \[\leadsto \color{blue}{-1 \cdot \frac{y \cdot \left(z - t\right)}{t}} \]
   11. Step-by-step derivation

       1. mul-1-neg 47.5%

          \[\leadsto \color{blue}{-\frac{y \cdot \left(z - t\right)}{t}} \]

       2. associate-/l* 63.1%

          \[\leadsto -\color{blue}{\frac{y}{\frac{t}{z - t}}} \]

       3. distribute-neg-frac 63.1%

          \[\leadsto \color{blue}{\frac{-y}{\frac{t}{z - t}}} \]

   12. Simplified 63.1%

       \[\leadsto \color{blue}{\frac{-y}{\frac{t}{z - t}}} \]

   if -6.39999999999999986e-112 < a < -2.6000000000000001e-199

   1. Initial program 55.6%

      \[x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \]
   2. Step-by-step derivation

      1. associate-*l/ 47.4%

         \[\leadsto x + \color{blue}{\frac{y - x}{a - t} \cdot \left(z - t\right)} \]

   3. Simplified 47.4%

      \[\leadsto \color{blue}{x + \frac{y - x}{a - t} \cdot \left(z - t\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in t around inf 69.9%

      \[\leadsto \color{blue}{\left(y + -1 \cdot \frac{z \cdot \left(y - x\right)}{t}\right) - -1 \cdot \frac{a \cdot \left(y - x\right)}{t}} \]
   6. Step-by-step derivation

      1. associate--l+ 69.9%

         \[\leadsto \color{blue}{y + \left(-1 \cdot \frac{z \cdot \left(y - x\right)}{t} - -1 \cdot \frac{a \cdot \left(y - x\right)}{t}\right)} \]

      2. associate-*r/ 69.9%

         \[\leadsto y + \left(\color{blue}{\frac{-1 \cdot \left(z \cdot \left(y - x\right)\right)}{t}} - -1 \cdot \frac{a \cdot \left(y - x\right)}{t}\right) \]

      3. associate-*r/ 69.9%

         \[\leadsto y + \left(\frac{-1 \cdot \left(z \cdot \left(y - x\right)\right)}{t} - \color{blue}{\frac{-1 \cdot \left(a \cdot \left(y - x\right)\right)}{t}}\right) \]

      4. div-sub 69.9%

         \[\leadsto y + \color{blue}{\frac{-1 \cdot \left(z \cdot \left(y - x\right)\right) - -1 \cdot \left(a \cdot \left(y - x\right)\right)}{t}} \]

      5. distribute-lft-out-- 69.9%

         \[\leadsto y + \frac{\color{blue}{-1 \cdot \left(z \cdot \left(y - x\right) - a \cdot \left(y - x\right)\right)}}{t} \]

      6. associate-*r/ 69.9%

         \[\leadsto y + \color{blue}{-1 \cdot \frac{z \cdot \left(y - x\right) - a \cdot \left(y - x\right)}{t}} \]

      7. mul-1-neg 69.9%

         \[\leadsto y + \color{blue}{\left(-\frac{z \cdot \left(y - x\right) - a \cdot \left(y - x\right)}{t}\right)} \]

      8. unsub-neg 69.9%

         \[\leadsto \color{blue}{y - \frac{z \cdot \left(y - x\right) - a \cdot \left(y - x\right)}{t}} \]

      9. distribute-rgt-out-- 69.9%

         \[\leadsto y - \frac{\color{blue}{\left(y - x\right) \cdot \left(z - a\right)}}{t} \]

      10. associate-/l* 84.4%

          \[\leadsto y - \color{blue}{\frac{y - x}{\frac{t}{z - a}}} \]

   7. Simplified 84.4%

      \[\leadsto \color{blue}{y - \frac{y - x}{\frac{t}{z - a}}} \]

   8. Taylor expanded in z around -inf 68.2%

      \[\leadsto \color{blue}{-1 \cdot \frac{z \cdot \left(y - x\right)}{t}} \]
   9. Step-by-step derivation

      1. associate-*r/ 68.2%

         \[\leadsto \color{blue}{\frac{-1 \cdot \left(z \cdot \left(y - x\right)\right)}{t}} \]

      2. mul-1-neg 68.2%

         \[\leadsto \frac{\color{blue}{-z \cdot \left(y - x\right)}}{t} \]

   10. Simplified 68.2%

       \[\leadsto \color{blue}{\frac{-z \cdot \left(y - x\right)}{t}} \]

   11. Taylor expanded in z around inf 68.2%

       \[\leadsto \color{blue}{\frac{z \cdot \left(x - y\right)}{t}} \]
   12. Step-by-step derivation

       1. associate-/l* 72.9%

          \[\leadsto \color{blue}{\frac{z}{\frac{t}{x - y}}} \]

   13. Simplified 72.9%

       \[\leadsto \color{blue}{\frac{z}{\frac{t}{x - y}}} \]
3. Recombined 3 regimes into one program.

4. Final simplification 66.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -9 \cdot 10^{+50}:\\ \;\;\;\;x + \frac{y}{\frac{a}{z}}\\ \mathbf{elif}\;a \leq -6.4 \cdot 10^{-112}:\\ \;\;\;\;\frac{-y}{\frac{t}{z - t}}\\ \mathbf{elif}\;a \leq -2.6 \cdot 10^{-199}:\\ \;\;\;\;\frac{z}{\frac{t}{x - y}}\\ \mathbf{elif}\;a \leq 9 \cdot 10^{+30}:\\ \;\;\;\;\frac{-y}{\frac{t}{z - t}}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{\frac{a}{z}}\\ \end{array} \]
5. Add Preprocessing

Alternative 14: 45.5% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + \frac{y}{\frac{a}{z}}\\ \mathbf{if}\;a \leq -2 \cdot 10^{-57}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq -1.9 \cdot 10^{-111}:\\ \;\;\;\;y\\ \mathbf{elif}\;a \leq -3.05 \cdot 10^{-201}:\\ \;\;\;\;\frac{x}{\frac{t}{z}}\\ \mathbf{elif}\;a \leq 1.35 \cdot 10^{+28}:\\ \;\;\;\;y\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ x (/ y (/ a z)))))
   (if (<= a -2e-57)
     t_1
     (if (<= a -1.9e-111)
       y
       (if (<= a -3.05e-201) (/ x (/ t z)) (if (<= a 1.35e+28) y t_1))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x + (y / (a / z));
	double tmp;
	if (a <= -2e-57) {
		tmp = t_1;
	} else if (a <= -1.9e-111) {
		tmp = y;
	} else if (a <= -3.05e-201) {
		tmp = x / (t / z);
	} else if (a <= 1.35e+28) {
		tmp = y;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x + (y / (a / z))
    if (a <= (-2d-57)) then
        tmp = t_1
    else if (a <= (-1.9d-111)) then
        tmp = y
    else if (a <= (-3.05d-201)) then
        tmp = x / (t / z)
    else if (a <= 1.35d+28) then
        tmp = y
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = x + (y / (a / z));
	double tmp;
	if (a <= -2e-57) {
		tmp = t_1;
	} else if (a <= -1.9e-111) {
		tmp = y;
	} else if (a <= -3.05e-201) {
		tmp = x / (t / z);
	} else if (a <= 1.35e+28) {
		tmp = y;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x + (y / (a / z))
	tmp = 0
	if a <= -2e-57:
		tmp = t_1
	elif a <= -1.9e-111:
		tmp = y
	elif a <= -3.05e-201:
		tmp = x / (t / z)
	elif a <= 1.35e+28:
		tmp = y
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x + Float64(y / Float64(a / z)))
	tmp = 0.0
	if (a <= -2e-57)
		tmp = t_1;
	elseif (a <= -1.9e-111)
		tmp = y;
	elseif (a <= -3.05e-201)
		tmp = Float64(x / Float64(t / z));
	elseif (a <= 1.35e+28)
		tmp = y;
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x + (y / (a / z));
	tmp = 0.0;
	if (a <= -2e-57)
		tmp = t_1;
	elseif (a <= -1.9e-111)
		tmp = y;
	elseif (a <= -3.05e-201)
		tmp = x / (t / z);
	elseif (a <= 1.35e+28)
		tmp = y;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x + N[(y / N[(a / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -2e-57], t$95$1, If[LessEqual[a, -1.9e-111], y, If[LessEqual[a, -3.05e-201], N[(x / N[(t / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 1.35e+28], y, t$95$1]]]]]

Derivation

1. Split input into 3 regimes

2. if a < -1.99999999999999991e-57 or 1.3500000000000001e28 < a

   1. Initial program 65.9%

      \[x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \]
   2. Step-by-step derivation

      1. associate-*l/ 82.7%

         \[\leadsto x + \color{blue}{\frac{y - x}{a - t} \cdot \left(z - t\right)} \]

   3. Simplified 82.7%

      \[\leadsto \color{blue}{x + \frac{y - x}{a - t} \cdot \left(z - t\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in t around 0 62.0%

      \[\leadsto \color{blue}{x + \frac{z \cdot \left(y - x\right)}{a}} \]

   6. Taylor expanded in y around inf 58.6%

      \[\leadsto x + \color{blue}{\frac{y \cdot z}{a}} \]
   7. Step-by-step derivation

      1. associate-/l* 63.7%

         \[\leadsto x + \color{blue}{\frac{y}{\frac{a}{z}}} \]

   8. Simplified 63.7%

      \[\leadsto x + \color{blue}{\frac{y}{\frac{a}{z}}} \]

   if -1.99999999999999991e-57 < a < -1.90000000000000011e-111 or -3.05000000000000013e-201 < a < 1.3500000000000001e28

   1. Initial program 64.4%

      \[x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \]
   2. Step-by-step derivation

      1. associate-*l/ 68.9%

         \[\leadsto x + \color{blue}{\frac{y - x}{a - t} \cdot \left(z - t\right)} \]

   3. Simplified 68.9%

      \[\leadsto \color{blue}{x + \frac{y - x}{a - t} \cdot \left(z - t\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in t around inf 45.2%

      \[\leadsto \color{blue}{y} \]

   if -1.90000000000000011e-111 < a < -3.05000000000000013e-201

   1. Initial program 55.6%

      \[x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \]
   2. Step-by-step derivation

      1. associate-*l/ 47.4%

         \[\leadsto x + \color{blue}{\frac{y - x}{a - t} \cdot \left(z - t\right)} \]

   3. Simplified 47.4%

      \[\leadsto \color{blue}{x + \frac{y - x}{a - t} \cdot \left(z - t\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in x around -inf 72.7%

      \[\leadsto \color{blue}{-1 \cdot \left(x \cdot \left(\frac{z}{a - t} - \left(1 + \frac{t}{a - t}\right)\right)\right)} \]
   6. Step-by-step derivation

      1. associate-*r* 72.7%

         \[\leadsto \color{blue}{\left(-1 \cdot x\right) \cdot \left(\frac{z}{a - t} - \left(1 + \frac{t}{a - t}\right)\right)} \]

      2. neg-mul-1 72.7%

         \[\leadsto \color{blue}{\left(-x\right)} \cdot \left(\frac{z}{a - t} - \left(1 + \frac{t}{a - t}\right)\right) \]

   7. Simplified 72.7%

      \[\leadsto \color{blue}{\left(-x\right) \cdot \left(\frac{z}{a - t} - \left(1 + \frac{t}{a - t}\right)\right)} \]

   8. Taylor expanded in a around 0 52.9%

      \[\leadsto \color{blue}{\frac{x \cdot z}{t}} \]
   9. Step-by-step derivation

      1. associate-/l* 62.7%

         \[\leadsto \color{blue}{\frac{x}{\frac{t}{z}}} \]

   10. Simplified 62.7%

       \[\leadsto \color{blue}{\frac{x}{\frac{t}{z}}} \]
3. Recombined 3 regimes into one program.

4. Final simplification 55.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -2 \cdot 10^{-57}:\\ \;\;\;\;x + \frac{y}{\frac{a}{z}}\\ \mathbf{elif}\;a \leq -1.9 \cdot 10^{-111}:\\ \;\;\;\;y\\ \mathbf{elif}\;a \leq -3.05 \cdot 10^{-201}:\\ \;\;\;\;\frac{x}{\frac{t}{z}}\\ \mathbf{elif}\;a \leq 1.35 \cdot 10^{+28}:\\ \;\;\;\;y\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{\frac{a}{z}}\\ \end{array} \]
5. Add Preprocessing

Alternative 15: 50.2% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{y}{t} \cdot \left(t - z\right)\\ t_2 := x + \frac{y}{\frac{a}{z}}\\ \mathbf{if}\;a \leq -5.5 \cdot 10^{-57}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;a \leq -7.6 \cdot 10^{-105}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq 6 \cdot 10^{-171}:\\ \;\;\;\;\frac{z}{\frac{t}{x - y}}\\ \mathbf{elif}\;a \leq 6.4 \cdot 10^{+83}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (* (/ y t) (- t z))) (t_2 (+ x (/ y (/ a z)))))
   (if (<= a -5.5e-57)
     t_2
     (if (<= a -7.6e-105)
       t_1
       (if (<= a 6e-171) (/ z (/ t (- x y))) (if (<= a 6.4e+83) t_1 t_2))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = (y / t) * (t - z);
	double t_2 = x + (y / (a / z));
	double tmp;
	if (a <= -5.5e-57) {
		tmp = t_2;
	} else if (a <= -7.6e-105) {
		tmp = t_1;
	} else if (a <= 6e-171) {
		tmp = z / (t / (x - y));
	} else if (a <= 6.4e+83) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = (y / t) * (t - z)
    t_2 = x + (y / (a / z))
    if (a <= (-5.5d-57)) then
        tmp = t_2
    else if (a <= (-7.6d-105)) then
        tmp = t_1
    else if (a <= 6d-171) then
        tmp = z / (t / (x - y))
    else if (a <= 6.4d+83) then
        tmp = t_1
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = (y / t) * (t - z);
	double t_2 = x + (y / (a / z));
	double tmp;
	if (a <= -5.5e-57) {
		tmp = t_2;
	} else if (a <= -7.6e-105) {
		tmp = t_1;
	} else if (a <= 6e-171) {
		tmp = z / (t / (x - y));
	} else if (a <= 6.4e+83) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = (y / t) * (t - z)
	t_2 = x + (y / (a / z))
	tmp = 0
	if a <= -5.5e-57:
		tmp = t_2
	elif a <= -7.6e-105:
		tmp = t_1
	elif a <= 6e-171:
		tmp = z / (t / (x - y))
	elif a <= 6.4e+83:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(Float64(y / t) * Float64(t - z))
	t_2 = Float64(x + Float64(y / Float64(a / z)))
	tmp = 0.0
	if (a <= -5.5e-57)
		tmp = t_2;
	elseif (a <= -7.6e-105)
		tmp = t_1;
	elseif (a <= 6e-171)
		tmp = Float64(z / Float64(t / Float64(x - y)));
	elseif (a <= 6.4e+83)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = (y / t) * (t - z);
	t_2 = x + (y / (a / z));
	tmp = 0.0;
	if (a <= -5.5e-57)
		tmp = t_2;
	elseif (a <= -7.6e-105)
		tmp = t_1;
	elseif (a <= 6e-171)
		tmp = z / (t / (x - y));
	elseif (a <= 6.4e+83)
		tmp = t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(N[(y / t), $MachinePrecision] * N[(t - z), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x + N[(y / N[(a / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -5.5e-57], t$95$2, If[LessEqual[a, -7.6e-105], t$95$1, If[LessEqual[a, 6e-171], N[(z / N[(t / N[(x - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 6.4e+83], t$95$1, t$95$2]]]]]]

Derivation

1. Split input into 3 regimes

2. if a < -5.50000000000000011e-57 or 6.3999999999999998e83 < a

   1. Initial program 65.4%

      \[x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \]
   2. Step-by-step derivation

      1. associate-*l/ 82.8%

         \[\leadsto x + \color{blue}{\frac{y - x}{a - t} \cdot \left(z - t\right)} \]

   3. Simplified 82.8%

      \[\leadsto \color{blue}{x + \frac{y - x}{a - t} \cdot \left(z - t\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in t around 0 61.3%

      \[\leadsto \color{blue}{x + \frac{z \cdot \left(y - x\right)}{a}} \]

   6. Taylor expanded in y around inf 60.0%

      \[\leadsto x + \color{blue}{\frac{y \cdot z}{a}} \]
   7. Step-by-step derivation

      1. associate-/l* 66.2%

         \[\leadsto x + \color{blue}{\frac{y}{\frac{a}{z}}} \]

   8. Simplified 66.2%

      \[\leadsto x + \color{blue}{\frac{y}{\frac{a}{z}}} \]

   if -5.50000000000000011e-57 < a < -7.5999999999999995e-105 or 5.9999999999999999e-171 < a < 6.3999999999999998e83

   1. Initial program 61.0%

      \[x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \]
   2. Step-by-step derivation

      1. associate-*l/ 76.2%

         \[\leadsto x + \color{blue}{\frac{y - x}{a - t} \cdot \left(z - t\right)} \]

   3. Simplified 76.2%

      \[\leadsto \color{blue}{x + \frac{y - x}{a - t} \cdot \left(z - t\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in x around 0 53.0%

      \[\leadsto \color{blue}{\frac{y \cdot \left(z - t\right)}{a - t}} \]
   6. Step-by-step derivation

      1. associate-/l* 67.0%

         \[\leadsto \color{blue}{\frac{y}{\frac{a - t}{z - t}}} \]

      2. associate-/r/ 64.0%

         \[\leadsto \color{blue}{\frac{y}{a - t} \cdot \left(z - t\right)} \]

   7. Simplified 64.0%

      \[\leadsto \color{blue}{\frac{y}{a - t} \cdot \left(z - t\right)} \]

   8. Taylor expanded in a around 0 57.7%

      \[\leadsto \color{blue}{\left(-1 \cdot \frac{y}{t}\right)} \cdot \left(z - t\right) \]
   9. Step-by-step derivation

      1. associate-*r/ 57.7%

         \[\leadsto \color{blue}{\frac{-1 \cdot y}{t}} \cdot \left(z - t\right) \]

      2. neg-mul-1 57.7%

         \[\leadsto \frac{\color{blue}{-y}}{t} \cdot \left(z - t\right) \]

   10. Simplified 57.7%

       \[\leadsto \color{blue}{\frac{-y}{t}} \cdot \left(z - t\right) \]

   if -7.5999999999999995e-105 < a < 5.9999999999999999e-171

   1. Initial program 66.3%

      \[x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \]
   2. Step-by-step derivation

      1. associate-*l/ 57.5%

         \[\leadsto x + \color{blue}{\frac{y - x}{a - t} \cdot \left(z - t\right)} \]

   3. Simplified 57.5%

      \[\leadsto \color{blue}{x + \frac{y - x}{a - t} \cdot \left(z - t\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in t around inf 78.6%

      \[\leadsto \color{blue}{\left(y + -1 \cdot \frac{z \cdot \left(y - x\right)}{t}\right) - -1 \cdot \frac{a \cdot \left(y - x\right)}{t}} \]
   6. Step-by-step derivation

      1. associate--l+ 78.6%

         \[\leadsto \color{blue}{y + \left(-1 \cdot \frac{z \cdot \left(y - x\right)}{t} - -1 \cdot \frac{a \cdot \left(y - x\right)}{t}\right)} \]

      2. associate-*r/ 78.6%

         \[\leadsto y + \left(\color{blue}{\frac{-1 \cdot \left(z \cdot \left(y - x\right)\right)}{t}} - -1 \cdot \frac{a \cdot \left(y - x\right)}{t}\right) \]

      3. associate-*r/ 78.6%

         \[\leadsto y + \left(\frac{-1 \cdot \left(z \cdot \left(y - x\right)\right)}{t} - \color{blue}{\frac{-1 \cdot \left(a \cdot \left(y - x\right)\right)}{t}}\right) \]

      4. div-sub 78.6%

         \[\leadsto y + \color{blue}{\frac{-1 \cdot \left(z \cdot \left(y - x\right)\right) - -1 \cdot \left(a \cdot \left(y - x\right)\right)}{t}} \]

      5. distribute-lft-out-- 78.6%

         \[\leadsto y + \frac{\color{blue}{-1 \cdot \left(z \cdot \left(y - x\right) - a \cdot \left(y - x\right)\right)}}{t} \]

      6. associate-*r/ 78.6%

         \[\leadsto y + \color{blue}{-1 \cdot \frac{z \cdot \left(y - x\right) - a \cdot \left(y - x\right)}{t}} \]

      7. mul-1-neg 78.6%

         \[\leadsto y + \color{blue}{\left(-\frac{z \cdot \left(y - x\right) - a \cdot \left(y - x\right)}{t}\right)} \]

      8. unsub-neg 78.6%

         \[\leadsto \color{blue}{y - \frac{z \cdot \left(y - x\right) - a \cdot \left(y - x\right)}{t}} \]

      9. distribute-rgt-out-- 78.6%

         \[\leadsto y - \frac{\color{blue}{\left(y - x\right) \cdot \left(z - a\right)}}{t} \]

      10. associate-/l* 87.4%

          \[\leadsto y - \color{blue}{\frac{y - x}{\frac{t}{z - a}}} \]

   7. Simplified 87.4%

      \[\leadsto \color{blue}{y - \frac{y - x}{\frac{t}{z - a}}} \]

   8. Taylor expanded in z around -inf 51.3%

      \[\leadsto \color{blue}{-1 \cdot \frac{z \cdot \left(y - x\right)}{t}} \]
   9. Step-by-step derivation

      1. associate-*r/ 51.3%

         \[\leadsto \color{blue}{\frac{-1 \cdot \left(z \cdot \left(y - x\right)\right)}{t}} \]

      2. mul-1-neg 51.3%

         \[\leadsto \frac{\color{blue}{-z \cdot \left(y - x\right)}}{t} \]

   10. Simplified 51.3%

       \[\leadsto \color{blue}{\frac{-z \cdot \left(y - x\right)}{t}} \]

   11. Taylor expanded in z around inf 51.3%

       \[\leadsto \color{blue}{\frac{z \cdot \left(x - y\right)}{t}} \]
   12. Step-by-step derivation

       1. associate-/l* 54.7%

          \[\leadsto \color{blue}{\frac{z}{\frac{t}{x - y}}} \]

   13. Simplified 54.7%

       \[\leadsto \color{blue}{\frac{z}{\frac{t}{x - y}}} \]
3. Recombined 3 regimes into one program.

4. Final simplification 60.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -5.5 \cdot 10^{-57}:\\ \;\;\;\;x + \frac{y}{\frac{a}{z}}\\ \mathbf{elif}\;a \leq -7.6 \cdot 10^{-105}:\\ \;\;\;\;\frac{y}{t} \cdot \left(t - z\right)\\ \mathbf{elif}\;a \leq 6 \cdot 10^{-171}:\\ \;\;\;\;\frac{z}{\frac{t}{x - y}}\\ \mathbf{elif}\;a \leq 6.4 \cdot 10^{+83}:\\ \;\;\;\;\frac{y}{t} \cdot \left(t - z\right)\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{\frac{a}{z}}\\ \end{array} \]
5. Add Preprocessing

Alternative 16: 73.8% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x - \frac{x - y}{\frac{a}{z - t}}\\ \mathbf{if}\;a \leq -6.8 \cdot 10^{+99}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq -4.6 \cdot 10^{-59}:\\ \;\;\;\;y \cdot \frac{z - t}{a - t}\\ \mathbf{elif}\;a \leq 1.06 \cdot 10^{+40}:\\ \;\;\;\;y + \frac{x - y}{\frac{t}{z}}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (- x (/ (- x y) (/ a (- z t))))))
   (if (<= a -6.8e+99)
     t_1
     (if (<= a -4.6e-59)
       (* y (/ (- z t) (- a t)))
       (if (<= a 1.06e+40) (+ y (/ (- x y) (/ t z))) t_1)))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x - ((x - y) / (a / (z - t)));
	double tmp;
	if (a <= -6.8e+99) {
		tmp = t_1;
	} else if (a <= -4.6e-59) {
		tmp = y * ((z - t) / (a - t));
	} else if (a <= 1.06e+40) {
		tmp = y + ((x - y) / (t / z));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x - ((x - y) / (a / (z - t)))
    if (a <= (-6.8d+99)) then
        tmp = t_1
    else if (a <= (-4.6d-59)) then
        tmp = y * ((z - t) / (a - t))
    else if (a <= 1.06d+40) then
        tmp = y + ((x - y) / (t / z))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = x - ((x - y) / (a / (z - t)));
	double tmp;
	if (a <= -6.8e+99) {
		tmp = t_1;
	} else if (a <= -4.6e-59) {
		tmp = y * ((z - t) / (a - t));
	} else if (a <= 1.06e+40) {
		tmp = y + ((x - y) / (t / z));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x - ((x - y) / (a / (z - t)))
	tmp = 0
	if a <= -6.8e+99:
		tmp = t_1
	elif a <= -4.6e-59:
		tmp = y * ((z - t) / (a - t))
	elif a <= 1.06e+40:
		tmp = y + ((x - y) / (t / z))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x - Float64(Float64(x - y) / Float64(a / Float64(z - t))))
	tmp = 0.0
	if (a <= -6.8e+99)
		tmp = t_1;
	elseif (a <= -4.6e-59)
		tmp = Float64(y * Float64(Float64(z - t) / Float64(a - t)));
	elseif (a <= 1.06e+40)
		tmp = Float64(y + Float64(Float64(x - y) / Float64(t / z)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x - ((x - y) / (a / (z - t)));
	tmp = 0.0;
	if (a <= -6.8e+99)
		tmp = t_1;
	elseif (a <= -4.6e-59)
		tmp = y * ((z - t) / (a - t));
	elseif (a <= 1.06e+40)
		tmp = y + ((x - y) / (t / z));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x - N[(N[(x - y), $MachinePrecision] / N[(a / N[(z - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[a, -6.8e+99], t$95$1, If[LessEqual[a, -4.6e-59], N[(y * N[(N[(z - t), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 1.06e+40], N[(y + N[(N[(x - y), $MachinePrecision] / N[(t / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Derivation

1. Split input into 3 regimes

2. if a < -6.79999999999999968e99 or 1.05999999999999996e40 < a

   1. Initial program 72.3%

      \[x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \]
   2. Step-by-step derivation

      1. associate-*l/ 90.7%

         \[\leadsto x + \color{blue}{\frac{y - x}{a - t} \cdot \left(z - t\right)} \]

   3. Simplified 90.7%

      \[\leadsto \color{blue}{x + \frac{y - x}{a - t} \cdot \left(z - t\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in a around inf 69.7%

      \[\leadsto \color{blue}{x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a}} \]
   6. Step-by-step derivation

      1. associate-/l* 87.6%

         \[\leadsto x + \color{blue}{\frac{y - x}{\frac{a}{z - t}}} \]

   7. Simplified 87.6%

      \[\leadsto \color{blue}{x + \frac{y - x}{\frac{a}{z - t}}} \]

   if -6.79999999999999968e99 < a < -4.59999999999999959e-59

   1. Initial program 48.7%

      \[x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \]
   2. Step-by-step derivation

      1. +-commutative 48.7%

         \[\leadsto \color{blue}{\frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} + x} \]

      2. associate-*l/ 61.5%

         \[\leadsto \color{blue}{\frac{y - x}{a - t} \cdot \left(z - t\right)} + x \]

      3. fma-def 62.4%

         \[\leadsto \color{blue}{\mathsf{fma}\left(\frac{y - x}{a - t}, z - t, x\right)} \]

   3. Simplified 62.4%

      \[\leadsto \color{blue}{\mathsf{fma}\left(\frac{y - x}{a - t}, z - t, x\right)} \]
   4. Add Preprocessing
   5. Step-by-step derivation

      1. fma-udef 61.5%

         \[\leadsto \color{blue}{\frac{y - x}{a - t} \cdot \left(z - t\right) + x} \]

      2. associate-/r/ 64.6%

         \[\leadsto \color{blue}{\frac{y - x}{\frac{a - t}{z - t}}} + x \]

      3. div-inv 64.3%

         \[\leadsto \color{blue}{\left(y - x\right) \cdot \frac{1}{\frac{a - t}{z - t}}} + x \]

      4. clear-num 64.5%

         \[\leadsto \left(y - x\right) \cdot \color{blue}{\frac{z - t}{a - t}} + x \]

   6. Applied egg-rr 64.5%

      \[\leadsto \color{blue}{\left(y - x\right) \cdot \frac{z - t}{a - t} + x} \]

   7. Taylor expanded in y around inf 63.0%

      \[\leadsto \color{blue}{y \cdot \left(\frac{z}{a - t} - \frac{t}{a - t}\right)} \]
   8. Step-by-step derivation

      1. div-sub 63.0%

         \[\leadsto y \cdot \color{blue}{\frac{z - t}{a - t}} \]

   9. Simplified 63.0%

      \[\leadsto \color{blue}{y \cdot \frac{z - t}{a - t}} \]

   if -4.59999999999999959e-59 < a < 1.05999999999999996e40

   1. Initial program 62.1%

      \[x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \]
   2. Step-by-step derivation

      1. associate-*l/ 64.7%

         \[\leadsto x + \color{blue}{\frac{y - x}{a - t} \cdot \left(z - t\right)} \]

   3. Simplified 64.7%

      \[\leadsto \color{blue}{x + \frac{y - x}{a - t} \cdot \left(z - t\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in t around inf 76.1%

      \[\leadsto \color{blue}{\left(y + -1 \cdot \frac{z \cdot \left(y - x\right)}{t}\right) - -1 \cdot \frac{a \cdot \left(y - x\right)}{t}} \]
   6. Step-by-step derivation

      1. associate--l+ 76.1%

         \[\leadsto \color{blue}{y + \left(-1 \cdot \frac{z \cdot \left(y - x\right)}{t} - -1 \cdot \frac{a \cdot \left(y - x\right)}{t}\right)} \]

      2. associate-*r/ 76.1%

         \[\leadsto y + \left(\color{blue}{\frac{-1 \cdot \left(z \cdot \left(y - x\right)\right)}{t}} - -1 \cdot \frac{a \cdot \left(y - x\right)}{t}\right) \]

      3. associate-*r/ 76.1%

         \[\leadsto y + \left(\frac{-1 \cdot \left(z \cdot \left(y - x\right)\right)}{t} - \color{blue}{\frac{-1 \cdot \left(a \cdot \left(y - x\right)\right)}{t}}\right) \]

      4. div-sub 78.5%

         \[\leadsto y + \color{blue}{\frac{-1 \cdot \left(z \cdot \left(y - x\right)\right) - -1 \cdot \left(a \cdot \left(y - x\right)\right)}{t}} \]

      5. distribute-lft-out-- 78.5%

         \[\leadsto y + \frac{\color{blue}{-1 \cdot \left(z \cdot \left(y - x\right) - a \cdot \left(y - x\right)\right)}}{t} \]

      6. associate-*r/ 78.5%

         \[\leadsto y + \color{blue}{-1 \cdot \frac{z \cdot \left(y - x\right) - a \cdot \left(y - x\right)}{t}} \]

      7. mul-1-neg 78.5%

         \[\leadsto y + \color{blue}{\left(-\frac{z \cdot \left(y - x\right) - a \cdot \left(y - x\right)}{t}\right)} \]

      8. unsub-neg 78.5%

         \[\leadsto \color{blue}{y - \frac{z \cdot \left(y - x\right) - a \cdot \left(y - x\right)}{t}} \]

      9. distribute-rgt-out-- 78.5%

         \[\leadsto y - \frac{\color{blue}{\left(y - x\right) \cdot \left(z - a\right)}}{t} \]

      10. associate-/l* 86.9%

          \[\leadsto y - \color{blue}{\frac{y - x}{\frac{t}{z - a}}} \]

   7. Simplified 86.9%

      \[\leadsto \color{blue}{y - \frac{y - x}{\frac{t}{z - a}}} \]

   8. Taylor expanded in z around inf 83.7%

      \[\leadsto y - \frac{y - x}{\color{blue}{\frac{t}{z}}} \]
3. Recombined 3 regimes into one program.

4. Final simplification 82.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -6.8 \cdot 10^{+99}:\\ \;\;\;\;x - \frac{x - y}{\frac{a}{z - t}}\\ \mathbf{elif}\;a \leq -4.6 \cdot 10^{-59}:\\ \;\;\;\;y \cdot \frac{z - t}{a - t}\\ \mathbf{elif}\;a \leq 1.06 \cdot 10^{+40}:\\ \;\;\;\;y + \frac{x - y}{\frac{t}{z}}\\ \mathbf{else}:\\ \;\;\;\;x - \frac{x - y}{\frac{a}{z - t}}\\ \end{array} \]
5. Add Preprocessing

Alternative 17: 70.7% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -9 \cdot 10^{+92}:\\ \;\;\;\;x - \frac{y}{a} \cdot \left(t - z\right)\\ \mathbf{elif}\;a \leq -1.5 \cdot 10^{-58}:\\ \;\;\;\;y \cdot \frac{z - t}{a - t}\\ \mathbf{elif}\;a \leq 8.6 \cdot 10^{+34}:\\ \;\;\;\;y + \frac{x - y}{\frac{t}{z}}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{z}{\frac{a}{y - x}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= a -9e+92)
   (- x (* (/ y a) (- t z)))
   (if (<= a -1.5e-58)
     (* y (/ (- z t) (- a t)))
     (if (<= a 8.6e+34) (+ y (/ (- x y) (/ t z))) (+ x (/ z (/ a (- y x))))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -9e+92) {
		tmp = x - ((y / a) * (t - z));
	} else if (a <= -1.5e-58) {
		tmp = y * ((z - t) / (a - t));
	} else if (a <= 8.6e+34) {
		tmp = y + ((x - y) / (t / z));
	} else {
		tmp = x + (z / (a / (y - x)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (a <= (-9d+92)) then
        tmp = x - ((y / a) * (t - z))
    else if (a <= (-1.5d-58)) then
        tmp = y * ((z - t) / (a - t))
    else if (a <= 8.6d+34) then
        tmp = y + ((x - y) / (t / z))
    else
        tmp = x + (z / (a / (y - x)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -9e+92) {
		tmp = x - ((y / a) * (t - z));
	} else if (a <= -1.5e-58) {
		tmp = y * ((z - t) / (a - t));
	} else if (a <= 8.6e+34) {
		tmp = y + ((x - y) / (t / z));
	} else {
		tmp = x + (z / (a / (y - x)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if a <= -9e+92:
		tmp = x - ((y / a) * (t - z))
	elif a <= -1.5e-58:
		tmp = y * ((z - t) / (a - t))
	elif a <= 8.6e+34:
		tmp = y + ((x - y) / (t / z))
	else:
		tmp = x + (z / (a / (y - x)))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (a <= -9e+92)
		tmp = Float64(x - Float64(Float64(y / a) * Float64(t - z)));
	elseif (a <= -1.5e-58)
		tmp = Float64(y * Float64(Float64(z - t) / Float64(a - t)));
	elseif (a <= 8.6e+34)
		tmp = Float64(y + Float64(Float64(x - y) / Float64(t / z)));
	else
		tmp = Float64(x + Float64(z / Float64(a / Float64(y - x))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (a <= -9e+92)
		tmp = x - ((y / a) * (t - z));
	elseif (a <= -1.5e-58)
		tmp = y * ((z - t) / (a - t));
	elseif (a <= 8.6e+34)
		tmp = y + ((x - y) / (t / z));
	else
		tmp = x + (z / (a / (y - x)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[a, -9e+92], N[(x - N[(N[(y / a), $MachinePrecision] * N[(t - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, -1.5e-58], N[(y * N[(N[(z - t), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 8.6e+34], N[(y + N[(N[(x - y), $MachinePrecision] / N[(t / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(z / N[(a / N[(y - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if a < -8.9999999999999998e92

   1. Initial program 77.9%

      \[x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \]
   2. Step-by-step derivation

      1. associate-*l/ 89.1%

         \[\leadsto x + \color{blue}{\frac{y - x}{a - t} \cdot \left(z - t\right)} \]

   3. Simplified 89.1%

      \[\leadsto \color{blue}{x + \frac{y - x}{a - t} \cdot \left(z - t\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in a around inf 72.8%

      \[\leadsto \color{blue}{x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a}} \]
   6. Step-by-step derivation

      1. associate-/l* 87.3%

         \[\leadsto x + \color{blue}{\frac{y - x}{\frac{a}{z - t}}} \]

   7. Simplified 87.3%

      \[\leadsto \color{blue}{x + \frac{y - x}{\frac{a}{z - t}}} \]

   8. Taylor expanded in y around inf 72.8%

      \[\leadsto x + \color{blue}{\frac{y \cdot \left(z - t\right)}{a}} \]
   9. Step-by-step derivation

      1. associate-/l* 80.7%

         \[\leadsto x + \color{blue}{\frac{y}{\frac{a}{z - t}}} \]

      2. associate-/r/ 73.8%

         \[\leadsto x + \color{blue}{\frac{y}{a} \cdot \left(z - t\right)} \]

   10. Simplified 73.8%

       \[\leadsto x + \color{blue}{\frac{y}{a} \cdot \left(z - t\right)} \]

   if -8.9999999999999998e92 < a < -1.50000000000000004e-58

   1. Initial program 48.6%

      \[x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \]
   2. Step-by-step derivation

      1. +-commutative 48.6%

         \[\leadsto \color{blue}{\frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} + x} \]

      2. associate-*l/ 62.2%

         \[\leadsto \color{blue}{\frac{y - x}{a - t} \cdot \left(z - t\right)} + x \]

      3. fma-def 63.0%

         \[\leadsto \color{blue}{\mathsf{fma}\left(\frac{y - x}{a - t}, z - t, x\right)} \]

   3. Simplified 63.0%

      \[\leadsto \color{blue}{\mathsf{fma}\left(\frac{y - x}{a - t}, z - t, x\right)} \]
   4. Add Preprocessing
   5. Step-by-step derivation

      1. fma-udef 62.2%

         \[\leadsto \color{blue}{\frac{y - x}{a - t} \cdot \left(z - t\right) + x} \]

      2. associate-/r/ 65.5%

         \[\leadsto \color{blue}{\frac{y - x}{\frac{a - t}{z - t}}} + x \]

      3. div-inv 65.3%

         \[\leadsto \color{blue}{\left(y - x\right) \cdot \frac{1}{\frac{a - t}{z - t}}} + x \]

      4. clear-num 65.4%

         \[\leadsto \left(y - x\right) \cdot \color{blue}{\frac{z - t}{a - t}} + x \]

   6. Applied egg-rr 65.4%

      \[\leadsto \color{blue}{\left(y - x\right) \cdot \frac{z - t}{a - t} + x} \]

   7. Taylor expanded in y around inf 63.9%

      \[\leadsto \color{blue}{y \cdot \left(\frac{z}{a - t} - \frac{t}{a - t}\right)} \]
   8. Step-by-step derivation

      1. div-sub 63.9%

         \[\leadsto y \cdot \color{blue}{\frac{z - t}{a - t}} \]

   9. Simplified 63.9%

      \[\leadsto \color{blue}{y \cdot \frac{z - t}{a - t}} \]

   if -1.50000000000000004e-58 < a < 8.59999999999999988e34

   1. Initial program 62.1%

      \[x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \]
   2. Step-by-step derivation

      1. associate-*l/ 64.7%

         \[\leadsto x + \color{blue}{\frac{y - x}{a - t} \cdot \left(z - t\right)} \]

   3. Simplified 64.7%

      \[\leadsto \color{blue}{x + \frac{y - x}{a - t} \cdot \left(z - t\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in t around inf 76.1%

      \[\leadsto \color{blue}{\left(y + -1 \cdot \frac{z \cdot \left(y - x\right)}{t}\right) - -1 \cdot \frac{a \cdot \left(y - x\right)}{t}} \]
   6. Step-by-step derivation

      1. associate--l+ 76.1%

         \[\leadsto \color{blue}{y + \left(-1 \cdot \frac{z \cdot \left(y - x\right)}{t} - -1 \cdot \frac{a \cdot \left(y - x\right)}{t}\right)} \]

      2. associate-*r/ 76.1%

         \[\leadsto y + \left(\color{blue}{\frac{-1 \cdot \left(z \cdot \left(y - x\right)\right)}{t}} - -1 \cdot \frac{a \cdot \left(y - x\right)}{t}\right) \]

      3. associate-*r/ 76.1%

         \[\leadsto y + \left(\frac{-1 \cdot \left(z \cdot \left(y - x\right)\right)}{t} - \color{blue}{\frac{-1 \cdot \left(a \cdot \left(y - x\right)\right)}{t}}\right) \]

      4. div-sub 78.5%

         \[\leadsto y + \color{blue}{\frac{-1 \cdot \left(z \cdot \left(y - x\right)\right) - -1 \cdot \left(a \cdot \left(y - x\right)\right)}{t}} \]

      5. distribute-lft-out-- 78.5%

         \[\leadsto y + \frac{\color{blue}{-1 \cdot \left(z \cdot \left(y - x\right) - a \cdot \left(y - x\right)\right)}}{t} \]

      6. associate-*r/ 78.5%

         \[\leadsto y + \color{blue}{-1 \cdot \frac{z \cdot \left(y - x\right) - a \cdot \left(y - x\right)}{t}} \]

      7. mul-1-neg 78.5%

         \[\leadsto y + \color{blue}{\left(-\frac{z \cdot \left(y - x\right) - a \cdot \left(y - x\right)}{t}\right)} \]

      8. unsub-neg 78.5%

         \[\leadsto \color{blue}{y - \frac{z \cdot \left(y - x\right) - a \cdot \left(y - x\right)}{t}} \]

      9. distribute-rgt-out-- 78.5%

         \[\leadsto y - \frac{\color{blue}{\left(y - x\right) \cdot \left(z - a\right)}}{t} \]

      10. associate-/l* 86.9%

          \[\leadsto y - \color{blue}{\frac{y - x}{\frac{t}{z - a}}} \]

   7. Simplified 86.9%

      \[\leadsto \color{blue}{y - \frac{y - x}{\frac{t}{z - a}}} \]

   8. Taylor expanded in z around inf 83.7%

      \[\leadsto y - \frac{y - x}{\color{blue}{\frac{t}{z}}} \]

   if 8.59999999999999988e34 < a

   1. Initial program 67.4%

      \[x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \]
   2. Step-by-step derivation

      1. associate-*l/ 90.5%

         \[\leadsto x + \color{blue}{\frac{y - x}{a - t} \cdot \left(z - t\right)} \]

   3. Simplified 90.5%

      \[\leadsto \color{blue}{x + \frac{y - x}{a - t} \cdot \left(z - t\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in t around 0 69.8%

      \[\leadsto \color{blue}{x + \frac{z \cdot \left(y - x\right)}{a}} \]
   6. Step-by-step derivation

      1. associate-/l* 83.2%

         \[\leadsto x + \color{blue}{\frac{z}{\frac{a}{y - x}}} \]

   7. Simplified 83.2%

      \[\leadsto \color{blue}{x + \frac{z}{\frac{a}{y - x}}} \]
3. Recombined 4 regimes into one program.

4. Final simplification 79.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -9 \cdot 10^{+92}:\\ \;\;\;\;x - \frac{y}{a} \cdot \left(t - z\right)\\ \mathbf{elif}\;a \leq -1.5 \cdot 10^{-58}:\\ \;\;\;\;y \cdot \frac{z - t}{a - t}\\ \mathbf{elif}\;a \leq 8.6 \cdot 10^{+34}:\\ \;\;\;\;y + \frac{x - y}{\frac{t}{z}}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{z}{\frac{a}{y - x}}\\ \end{array} \]
5. Add Preprocessing

Alternative 18: 87.1% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -8.2 \cdot 10^{+167} \lor \neg \left(t \leq 3.71 \cdot 10^{+90}\right):\\ \;\;\;\;y + \frac{x - y}{\frac{t}{z - a}}\\ \mathbf{else}:\\ \;\;\;\;x - \left(z - t\right) \cdot \frac{x - y}{a - t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= t -8.2e+167) (not (<= t 3.71e+90)))
   (+ y (/ (- x y) (/ t (- z a))))
   (- x (* (- z t) (/ (- x y) (- a t))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((t <= -8.2e+167) || !(t <= 3.71e+90)) {
		tmp = y + ((x - y) / (t / (z - a)));
	} else {
		tmp = x - ((z - t) * ((x - y) / (a - t)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((t <= (-8.2d+167)) .or. (.not. (t <= 3.71d+90))) then
        tmp = y + ((x - y) / (t / (z - a)))
    else
        tmp = x - ((z - t) * ((x - y) / (a - t)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((t <= -8.2e+167) || !(t <= 3.71e+90)) {
		tmp = y + ((x - y) / (t / (z - a)));
	} else {
		tmp = x - ((z - t) * ((x - y) / (a - t)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (t <= -8.2e+167) or not (t <= 3.71e+90):
		tmp = y + ((x - y) / (t / (z - a)))
	else:
		tmp = x - ((z - t) * ((x - y) / (a - t)))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((t <= -8.2e+167) || !(t <= 3.71e+90))
		tmp = Float64(y + Float64(Float64(x - y) / Float64(t / Float64(z - a))));
	else
		tmp = Float64(x - Float64(Float64(z - t) * Float64(Float64(x - y) / Float64(a - t))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((t <= -8.2e+167) || ~((t <= 3.71e+90)))
		tmp = y + ((x - y) / (t / (z - a)));
	else
		tmp = x - ((z - t) * ((x - y) / (a - t)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[t, -8.2e+167], N[Not[LessEqual[t, 3.71e+90]], $MachinePrecision]], N[(y + N[(N[(x - y), $MachinePrecision] / N[(t / N[(z - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x - N[(N[(z - t), $MachinePrecision] * N[(N[(x - y), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -8.2e167 or 3.7100000000000001e90 < t

   1. Initial program 23.6%

      \[x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \]
   2. Step-by-step derivation

      1. associate-*l/ 52.2%

         \[\leadsto x + \color{blue}{\frac{y - x}{a - t} \cdot \left(z - t\right)} \]

   3. Simplified 52.2%

      \[\leadsto \color{blue}{x + \frac{y - x}{a - t} \cdot \left(z - t\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in t around inf 64.6%

      \[\leadsto \color{blue}{\left(y + -1 \cdot \frac{z \cdot \left(y - x\right)}{t}\right) - -1 \cdot \frac{a \cdot \left(y - x\right)}{t}} \]
   6. Step-by-step derivation

      1. associate--l+ 64.6%

         \[\leadsto \color{blue}{y + \left(-1 \cdot \frac{z \cdot \left(y - x\right)}{t} - -1 \cdot \frac{a \cdot \left(y - x\right)}{t}\right)} \]

      2. associate-*r/ 64.6%

         \[\leadsto y + \left(\color{blue}{\frac{-1 \cdot \left(z \cdot \left(y - x\right)\right)}{t}} - -1 \cdot \frac{a \cdot \left(y - x\right)}{t}\right) \]

      3. associate-*r/ 64.6%

         \[\leadsto y + \left(\frac{-1 \cdot \left(z \cdot \left(y - x\right)\right)}{t} - \color{blue}{\frac{-1 \cdot \left(a \cdot \left(y - x\right)\right)}{t}}\right) \]

      4. div-sub 64.6%

         \[\leadsto y + \color{blue}{\frac{-1 \cdot \left(z \cdot \left(y - x\right)\right) - -1 \cdot \left(a \cdot \left(y - x\right)\right)}{t}} \]

      5. distribute-lft-out-- 64.6%

         \[\leadsto y + \frac{\color{blue}{-1 \cdot \left(z \cdot \left(y - x\right) - a \cdot \left(y - x\right)\right)}}{t} \]

      6. associate-*r/ 64.6%

         \[\leadsto y + \color{blue}{-1 \cdot \frac{z \cdot \left(y - x\right) - a \cdot \left(y - x\right)}{t}} \]

      7. mul-1-neg 64.6%

         \[\leadsto y + \color{blue}{\left(-\frac{z \cdot \left(y - x\right) - a \cdot \left(y - x\right)}{t}\right)} \]

      8. unsub-neg 64.6%

         \[\leadsto \color{blue}{y - \frac{z \cdot \left(y - x\right) - a \cdot \left(y - x\right)}{t}} \]

      9. distribute-rgt-out-- 64.7%

         \[\leadsto y - \frac{\color{blue}{\left(y - x\right) \cdot \left(z - a\right)}}{t} \]

      10. associate-/l* 87.3%

          \[\leadsto y - \color{blue}{\frac{y - x}{\frac{t}{z - a}}} \]

   7. Simplified 87.3%

      \[\leadsto \color{blue}{y - \frac{y - x}{\frac{t}{z - a}}} \]

   if -8.2e167 < t < 3.7100000000000001e90

   1. Initial program 83.1%

      \[x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \]
   2. Step-by-step derivation

      1. associate-*l/ 84.4%

         \[\leadsto x + \color{blue}{\frac{y - x}{a - t} \cdot \left(z - t\right)} \]

   3. Simplified 84.4%

      \[\leadsto \color{blue}{x + \frac{y - x}{a - t} \cdot \left(z - t\right)} \]
   4. Add Preprocessing
3. Recombined 2 regimes into one program.

4. Final simplification 85.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -8.2 \cdot 10^{+167} \lor \neg \left(t \leq 3.71 \cdot 10^{+90}\right):\\ \;\;\;\;y + \frac{x - y}{\frac{t}{z - a}}\\ \mathbf{else}:\\ \;\;\;\;x - \left(z - t\right) \cdot \frac{x - y}{a - t}\\ \end{array} \]
5. Add Preprocessing

Alternative 19: 89.3% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -3.55 \cdot 10^{+165} \lor \neg \left(t \leq 4 \cdot 10^{+142}\right):\\ \;\;\;\;y + \frac{x - y}{\frac{t}{z - a}}\\ \mathbf{else}:\\ \;\;\;\;x - \frac{z - t}{a - t} \cdot \left(x - y\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= t -3.55e+165) (not (<= t 4e+142)))
   (+ y (/ (- x y) (/ t (- z a))))
   (- x (* (/ (- z t) (- a t)) (- x y)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((t <= -3.55e+165) || !(t <= 4e+142)) {
		tmp = y + ((x - y) / (t / (z - a)));
	} else {
		tmp = x - (((z - t) / (a - t)) * (x - y));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((t <= (-3.55d+165)) .or. (.not. (t <= 4d+142))) then
        tmp = y + ((x - y) / (t / (z - a)))
    else
        tmp = x - (((z - t) / (a - t)) * (x - y))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((t <= -3.55e+165) || !(t <= 4e+142)) {
		tmp = y + ((x - y) / (t / (z - a)));
	} else {
		tmp = x - (((z - t) / (a - t)) * (x - y));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (t <= -3.55e+165) or not (t <= 4e+142):
		tmp = y + ((x - y) / (t / (z - a)))
	else:
		tmp = x - (((z - t) / (a - t)) * (x - y))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((t <= -3.55e+165) || !(t <= 4e+142))
		tmp = Float64(y + Float64(Float64(x - y) / Float64(t / Float64(z - a))));
	else
		tmp = Float64(x - Float64(Float64(Float64(z - t) / Float64(a - t)) * Float64(x - y)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((t <= -3.55e+165) || ~((t <= 4e+142)))
		tmp = y + ((x - y) / (t / (z - a)));
	else
		tmp = x - (((z - t) / (a - t)) * (x - y));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[t, -3.55e+165], N[Not[LessEqual[t, 4e+142]], $MachinePrecision]], N[(y + N[(N[(x - y), $MachinePrecision] / N[(t / N[(z - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x - N[(N[(N[(z - t), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision] * N[(x - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -3.54999999999999988e165 or 4.0000000000000002e142 < t

   1. Initial program 20.3%

      \[x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \]
   2. Step-by-step derivation

      1. associate-*l/ 49.6%

         \[\leadsto x + \color{blue}{\frac{y - x}{a - t} \cdot \left(z - t\right)} \]

   3. Simplified 49.6%

      \[\leadsto \color{blue}{x + \frac{y - x}{a - t} \cdot \left(z - t\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in t around inf 63.8%

      \[\leadsto \color{blue}{\left(y + -1 \cdot \frac{z \cdot \left(y - x\right)}{t}\right) - -1 \cdot \frac{a \cdot \left(y - x\right)}{t}} \]
   6. Step-by-step derivation

      1. associate--l+ 63.8%

         \[\leadsto \color{blue}{y + \left(-1 \cdot \frac{z \cdot \left(y - x\right)}{t} - -1 \cdot \frac{a \cdot \left(y - x\right)}{t}\right)} \]

      2. associate-*r/ 63.8%

         \[\leadsto y + \left(\color{blue}{\frac{-1 \cdot \left(z \cdot \left(y - x\right)\right)}{t}} - -1 \cdot \frac{a \cdot \left(y - x\right)}{t}\right) \]

      3. associate-*r/ 63.8%

         \[\leadsto y + \left(\frac{-1 \cdot \left(z \cdot \left(y - x\right)\right)}{t} - \color{blue}{\frac{-1 \cdot \left(a \cdot \left(y - x\right)\right)}{t}}\right) \]

      4. div-sub 63.8%

         \[\leadsto y + \color{blue}{\frac{-1 \cdot \left(z \cdot \left(y - x\right)\right) - -1 \cdot \left(a \cdot \left(y - x\right)\right)}{t}} \]

      5. distribute-lft-out-- 63.8%

         \[\leadsto y + \frac{\color{blue}{-1 \cdot \left(z \cdot \left(y - x\right) - a \cdot \left(y - x\right)\right)}}{t} \]

      6. associate-*r/ 63.8%

         \[\leadsto y + \color{blue}{-1 \cdot \frac{z \cdot \left(y - x\right) - a \cdot \left(y - x\right)}{t}} \]

      7. mul-1-neg 63.8%

         \[\leadsto y + \color{blue}{\left(-\frac{z \cdot \left(y - x\right) - a \cdot \left(y - x\right)}{t}\right)} \]

      8. unsub-neg 63.8%

         \[\leadsto \color{blue}{y - \frac{z \cdot \left(y - x\right) - a \cdot \left(y - x\right)}{t}} \]

      9. distribute-rgt-out-- 63.8%

         \[\leadsto y - \frac{\color{blue}{\left(y - x\right) \cdot \left(z - a\right)}}{t} \]

      10. associate-/l* 90.3%

          \[\leadsto y - \color{blue}{\frac{y - x}{\frac{t}{z - a}}} \]

   7. Simplified 90.3%

      \[\leadsto \color{blue}{y - \frac{y - x}{\frac{t}{z - a}}} \]

   if -3.54999999999999988e165 < t < 4.0000000000000002e142

   1. Initial program 79.5%

      \[x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \]
   2. Step-by-step derivation

      1. +-commutative 79.5%

         \[\leadsto \color{blue}{\frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} + x} \]

      2. associate-*l/ 82.8%

         \[\leadsto \color{blue}{\frac{y - x}{a - t} \cdot \left(z - t\right)} + x \]

      3. fma-def 82.9%

         \[\leadsto \color{blue}{\mathsf{fma}\left(\frac{y - x}{a - t}, z - t, x\right)} \]

   3. Simplified 82.9%

      \[\leadsto \color{blue}{\mathsf{fma}\left(\frac{y - x}{a - t}, z - t, x\right)} \]
   4. Add Preprocessing
   5. Step-by-step derivation

      1. fma-udef 82.8%

         \[\leadsto \color{blue}{\frac{y - x}{a - t} \cdot \left(z - t\right) + x} \]

      2. associate-/r/ 91.8%

         \[\leadsto \color{blue}{\frac{y - x}{\frac{a - t}{z - t}}} + x \]

      3. div-inv 91.8%

         \[\leadsto \color{blue}{\left(y - x\right) \cdot \frac{1}{\frac{a - t}{z - t}}} + x \]

      4. clear-num 91.8%

         \[\leadsto \left(y - x\right) \cdot \color{blue}{\frac{z - t}{a - t}} + x \]

   6. Applied egg-rr 91.8%

      \[\leadsto \color{blue}{\left(y - x\right) \cdot \frac{z - t}{a - t} + x} \]
3. Recombined 2 regimes into one program.

4. Final simplification 91.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -3.55 \cdot 10^{+165} \lor \neg \left(t \leq 4 \cdot 10^{+142}\right):\\ \;\;\;\;y + \frac{x - y}{\frac{t}{z - a}}\\ \mathbf{else}:\\ \;\;\;\;x - \frac{z - t}{a - t} \cdot \left(x - y\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 20: 37.5% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -3.8 \cdot 10^{+92}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq -9 \cdot 10^{-111}:\\ \;\;\;\;y\\ \mathbf{elif}\;a \leq -1.26 \cdot 10^{-200}:\\ \;\;\;\;z \cdot \frac{x}{t}\\ \mathbf{elif}\;a \leq 1.45 \cdot 10^{+84}:\\ \;\;\;\;y\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= a -3.8e+92)
   x
   (if (<= a -9e-111)
     y
     (if (<= a -1.26e-200) (* z (/ x t)) (if (<= a 1.45e+84) y x)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -3.8e+92) {
		tmp = x;
	} else if (a <= -9e-111) {
		tmp = y;
	} else if (a <= -1.26e-200) {
		tmp = z * (x / t);
	} else if (a <= 1.45e+84) {
		tmp = y;
	} else {
		tmp = x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (a <= (-3.8d+92)) then
        tmp = x
    else if (a <= (-9d-111)) then
        tmp = y
    else if (a <= (-1.26d-200)) then
        tmp = z * (x / t)
    else if (a <= 1.45d+84) then
        tmp = y
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -3.8e+92) {
		tmp = x;
	} else if (a <= -9e-111) {
		tmp = y;
	} else if (a <= -1.26e-200) {
		tmp = z * (x / t);
	} else if (a <= 1.45e+84) {
		tmp = y;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if a <= -3.8e+92:
		tmp = x
	elif a <= -9e-111:
		tmp = y
	elif a <= -1.26e-200:
		tmp = z * (x / t)
	elif a <= 1.45e+84:
		tmp = y
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (a <= -3.8e+92)
		tmp = x;
	elseif (a <= -9e-111)
		tmp = y;
	elseif (a <= -1.26e-200)
		tmp = Float64(z * Float64(x / t));
	elseif (a <= 1.45e+84)
		tmp = y;
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (a <= -3.8e+92)
		tmp = x;
	elseif (a <= -9e-111)
		tmp = y;
	elseif (a <= -1.26e-200)
		tmp = z * (x / t);
	elseif (a <= 1.45e+84)
		tmp = y;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[a, -3.8e+92], x, If[LessEqual[a, -9e-111], y, If[LessEqual[a, -1.26e-200], N[(z * N[(x / t), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 1.45e+84], y, x]]]]

Derivation

1. Split input into 3 regimes

2. if a < -3.8e92 or 1.44999999999999994e84 < a

   1. Initial program 70.4%

      \[x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \]
   2. Step-by-step derivation

      1. associate-*l/ 89.0%

         \[\leadsto x + \color{blue}{\frac{y - x}{a - t} \cdot \left(z - t\right)} \]

   3. Simplified 89.0%

      \[\leadsto \color{blue}{x + \frac{y - x}{a - t} \cdot \left(z - t\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in a around inf 60.0%

      \[\leadsto \color{blue}{x} \]

   if -3.8e92 < a < -8.99999999999999987e-111 or -1.26e-200 < a < 1.44999999999999994e84

   1. Initial program 61.8%

      \[x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \]
   2. Step-by-step derivation

      1. associate-*l/ 68.4%

         \[\leadsto x + \color{blue}{\frac{y - x}{a - t} \cdot \left(z - t\right)} \]

   3. Simplified 68.4%

      \[\leadsto \color{blue}{x + \frac{y - x}{a - t} \cdot \left(z - t\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in t around inf 41.0%

      \[\leadsto \color{blue}{y} \]

   if -8.99999999999999987e-111 < a < -1.26e-200

   1. Initial program 55.6%

      \[x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \]
   2. Step-by-step derivation

      1. associate-*l/ 47.4%

         \[\leadsto x + \color{blue}{\frac{y - x}{a - t} \cdot \left(z - t\right)} \]

   3. Simplified 47.4%

      \[\leadsto \color{blue}{x + \frac{y - x}{a - t} \cdot \left(z - t\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in x around -inf 72.7%

      \[\leadsto \color{blue}{-1 \cdot \left(x \cdot \left(\frac{z}{a - t} - \left(1 + \frac{t}{a - t}\right)\right)\right)} \]
   6. Step-by-step derivation

      1. associate-*r* 72.7%

         \[\leadsto \color{blue}{\left(-1 \cdot x\right) \cdot \left(\frac{z}{a - t} - \left(1 + \frac{t}{a - t}\right)\right)} \]

      2. neg-mul-1 72.7%

         \[\leadsto \color{blue}{\left(-x\right)} \cdot \left(\frac{z}{a - t} - \left(1 + \frac{t}{a - t}\right)\right) \]

   7. Simplified 72.7%

      \[\leadsto \color{blue}{\left(-x\right) \cdot \left(\frac{z}{a - t} - \left(1 + \frac{t}{a - t}\right)\right)} \]

   8. Taylor expanded in a around 0 52.9%

      \[\leadsto \color{blue}{\frac{x \cdot z}{t}} \]
   9. Step-by-step derivation

      1. associate-/l* 62.7%

         \[\leadsto \color{blue}{\frac{x}{\frac{t}{z}}} \]

   10. Simplified 62.7%

       \[\leadsto \color{blue}{\frac{x}{\frac{t}{z}}} \]
   11. Step-by-step derivation

       1. associate-/r/ 57.8%

          \[\leadsto \color{blue}{\frac{x}{t} \cdot z} \]

   12. Applied egg-rr 57.8%

       \[\leadsto \color{blue}{\frac{x}{t} \cdot z} \]
3. Recombined 3 regimes into one program.

4. Final simplification 49.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -3.8 \cdot 10^{+92}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq -9 \cdot 10^{-111}:\\ \;\;\;\;y\\ \mathbf{elif}\;a \leq -1.26 \cdot 10^{-200}:\\ \;\;\;\;z \cdot \frac{x}{t}\\ \mathbf{elif}\;a \leq 1.45 \cdot 10^{+84}:\\ \;\;\;\;y\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 21: 37.7% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -2.6 \cdot 10^{+92}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq -7 \cdot 10^{-109}:\\ \;\;\;\;y\\ \mathbf{elif}\;a \leq -7.8 \cdot 10^{-203}:\\ \;\;\;\;\frac{x}{\frac{t}{z}}\\ \mathbf{elif}\;a \leq 1.45 \cdot 10^{+84}:\\ \;\;\;\;y\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= a -2.6e+92)
   x
   (if (<= a -7e-109)
     y
     (if (<= a -7.8e-203) (/ x (/ t z)) (if (<= a 1.45e+84) y x)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -2.6e+92) {
		tmp = x;
	} else if (a <= -7e-109) {
		tmp = y;
	} else if (a <= -7.8e-203) {
		tmp = x / (t / z);
	} else if (a <= 1.45e+84) {
		tmp = y;
	} else {
		tmp = x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (a <= (-2.6d+92)) then
        tmp = x
    else if (a <= (-7d-109)) then
        tmp = y
    else if (a <= (-7.8d-203)) then
        tmp = x / (t / z)
    else if (a <= 1.45d+84) then
        tmp = y
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -2.6e+92) {
		tmp = x;
	} else if (a <= -7e-109) {
		tmp = y;
	} else if (a <= -7.8e-203) {
		tmp = x / (t / z);
	} else if (a <= 1.45e+84) {
		tmp = y;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if a <= -2.6e+92:
		tmp = x
	elif a <= -7e-109:
		tmp = y
	elif a <= -7.8e-203:
		tmp = x / (t / z)
	elif a <= 1.45e+84:
		tmp = y
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (a <= -2.6e+92)
		tmp = x;
	elseif (a <= -7e-109)
		tmp = y;
	elseif (a <= -7.8e-203)
		tmp = Float64(x / Float64(t / z));
	elseif (a <= 1.45e+84)
		tmp = y;
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (a <= -2.6e+92)
		tmp = x;
	elseif (a <= -7e-109)
		tmp = y;
	elseif (a <= -7.8e-203)
		tmp = x / (t / z);
	elseif (a <= 1.45e+84)
		tmp = y;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[a, -2.6e+92], x, If[LessEqual[a, -7e-109], y, If[LessEqual[a, -7.8e-203], N[(x / N[(t / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[a, 1.45e+84], y, x]]]]

Derivation

1. Split input into 3 regimes

2. if a < -2.5999999999999999e92 or 1.44999999999999994e84 < a

   1. Initial program 70.4%

      \[x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \]
   2. Step-by-step derivation

      1. associate-*l/ 89.0%

         \[\leadsto x + \color{blue}{\frac{y - x}{a - t} \cdot \left(z - t\right)} \]

   3. Simplified 89.0%

      \[\leadsto \color{blue}{x + \frac{y - x}{a - t} \cdot \left(z - t\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in a around inf 60.0%

      \[\leadsto \color{blue}{x} \]

   if -2.5999999999999999e92 < a < -7e-109 or -7.7999999999999998e-203 < a < 1.44999999999999994e84

   1. Initial program 61.8%

      \[x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \]
   2. Step-by-step derivation

      1. associate-*l/ 68.4%

         \[\leadsto x + \color{blue}{\frac{y - x}{a - t} \cdot \left(z - t\right)} \]

   3. Simplified 68.4%

      \[\leadsto \color{blue}{x + \frac{y - x}{a - t} \cdot \left(z - t\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in t around inf 41.0%

      \[\leadsto \color{blue}{y} \]

   if -7e-109 < a < -7.7999999999999998e-203

   1. Initial program 55.6%

      \[x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \]
   2. Step-by-step derivation

      1. associate-*l/ 47.4%

         \[\leadsto x + \color{blue}{\frac{y - x}{a - t} \cdot \left(z - t\right)} \]

   3. Simplified 47.4%

      \[\leadsto \color{blue}{x + \frac{y - x}{a - t} \cdot \left(z - t\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in x around -inf 72.7%

      \[\leadsto \color{blue}{-1 \cdot \left(x \cdot \left(\frac{z}{a - t} - \left(1 + \frac{t}{a - t}\right)\right)\right)} \]
   6. Step-by-step derivation

      1. associate-*r* 72.7%

         \[\leadsto \color{blue}{\left(-1 \cdot x\right) \cdot \left(\frac{z}{a - t} - \left(1 + \frac{t}{a - t}\right)\right)} \]

      2. neg-mul-1 72.7%

         \[\leadsto \color{blue}{\left(-x\right)} \cdot \left(\frac{z}{a - t} - \left(1 + \frac{t}{a - t}\right)\right) \]

   7. Simplified 72.7%

      \[\leadsto \color{blue}{\left(-x\right) \cdot \left(\frac{z}{a - t} - \left(1 + \frac{t}{a - t}\right)\right)} \]

   8. Taylor expanded in a around 0 52.9%

      \[\leadsto \color{blue}{\frac{x \cdot z}{t}} \]
   9. Step-by-step derivation

      1. associate-/l* 62.7%

         \[\leadsto \color{blue}{\frac{x}{\frac{t}{z}}} \]

   10. Simplified 62.7%

       \[\leadsto \color{blue}{\frac{x}{\frac{t}{z}}} \]
3. Recombined 3 regimes into one program.

4. Final simplification 49.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -2.6 \cdot 10^{+92}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq -7 \cdot 10^{-109}:\\ \;\;\;\;y\\ \mathbf{elif}\;a \leq -7.8 \cdot 10^{-203}:\\ \;\;\;\;\frac{x}{\frac{t}{z}}\\ \mathbf{elif}\;a \leq 1.45 \cdot 10^{+84}:\\ \;\;\;\;y\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 22: 75.4% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -4.8 \cdot 10^{+95} \lor \neg \left(a \leq 2.6 \cdot 10^{+43}\right):\\ \;\;\;\;x - \frac{x - y}{\frac{a}{z - t}}\\ \mathbf{else}:\\ \;\;\;\;y + \frac{x - y}{\frac{t}{z - a}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= a -4.8e+95) (not (<= a 2.6e+43)))
   (- x (/ (- x y) (/ a (- z t))))
   (+ y (/ (- x y) (/ t (- z a))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((a <= -4.8e+95) || !(a <= 2.6e+43)) {
		tmp = x - ((x - y) / (a / (z - t)));
	} else {
		tmp = y + ((x - y) / (t / (z - a)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((a <= (-4.8d+95)) .or. (.not. (a <= 2.6d+43))) then
        tmp = x - ((x - y) / (a / (z - t)))
    else
        tmp = y + ((x - y) / (t / (z - a)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((a <= -4.8e+95) || !(a <= 2.6e+43)) {
		tmp = x - ((x - y) / (a / (z - t)));
	} else {
		tmp = y + ((x - y) / (t / (z - a)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (a <= -4.8e+95) or not (a <= 2.6e+43):
		tmp = x - ((x - y) / (a / (z - t)))
	else:
		tmp = y + ((x - y) / (t / (z - a)))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((a <= -4.8e+95) || !(a <= 2.6e+43))
		tmp = Float64(x - Float64(Float64(x - y) / Float64(a / Float64(z - t))));
	else
		tmp = Float64(y + Float64(Float64(x - y) / Float64(t / Float64(z - a))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((a <= -4.8e+95) || ~((a <= 2.6e+43)))
		tmp = x - ((x - y) / (a / (z - t)));
	else
		tmp = y + ((x - y) / (t / (z - a)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[a, -4.8e+95], N[Not[LessEqual[a, 2.6e+43]], $MachinePrecision]], N[(x - N[(N[(x - y), $MachinePrecision] / N[(a / N[(z - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(y + N[(N[(x - y), $MachinePrecision] / N[(t / N[(z - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if a < -4.8000000000000001e95 or 2.60000000000000021e43 < a

   1. Initial program 72.6%

      \[x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \]
   2. Step-by-step derivation

      1. associate-*l/ 90.8%

         \[\leadsto x + \color{blue}{\frac{y - x}{a - t} \cdot \left(z - t\right)} \]

   3. Simplified 90.8%

      \[\leadsto \color{blue}{x + \frac{y - x}{a - t} \cdot \left(z - t\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in a around inf 70.0%

      \[\leadsto \color{blue}{x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a}} \]
   6. Step-by-step derivation

      1. associate-/l* 87.7%

         \[\leadsto x + \color{blue}{\frac{y - x}{\frac{a}{z - t}}} \]

   7. Simplified 87.7%

      \[\leadsto \color{blue}{x + \frac{y - x}{\frac{a}{z - t}}} \]

   if -4.8000000000000001e95 < a < 2.60000000000000021e43

   1. Initial program 59.3%

      \[x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \]
   2. Step-by-step derivation

      1. associate-*l/ 63.8%

         \[\leadsto x + \color{blue}{\frac{y - x}{a - t} \cdot \left(z - t\right)} \]

   3. Simplified 63.8%

      \[\leadsto \color{blue}{x + \frac{y - x}{a - t} \cdot \left(z - t\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in t around inf 71.2%

      \[\leadsto \color{blue}{\left(y + -1 \cdot \frac{z \cdot \left(y - x\right)}{t}\right) - -1 \cdot \frac{a \cdot \left(y - x\right)}{t}} \]
   6. Step-by-step derivation

      1. associate--l+ 71.2%

         \[\leadsto \color{blue}{y + \left(-1 \cdot \frac{z \cdot \left(y - x\right)}{t} - -1 \cdot \frac{a \cdot \left(y - x\right)}{t}\right)} \]

      2. associate-*r/ 71.2%

         \[\leadsto y + \left(\color{blue}{\frac{-1 \cdot \left(z \cdot \left(y - x\right)\right)}{t}} - -1 \cdot \frac{a \cdot \left(y - x\right)}{t}\right) \]

      3. associate-*r/ 71.2%

         \[\leadsto y + \left(\frac{-1 \cdot \left(z \cdot \left(y - x\right)\right)}{t} - \color{blue}{\frac{-1 \cdot \left(a \cdot \left(y - x\right)\right)}{t}}\right) \]

      4. div-sub 73.2%

         \[\leadsto y + \color{blue}{\frac{-1 \cdot \left(z \cdot \left(y - x\right)\right) - -1 \cdot \left(a \cdot \left(y - x\right)\right)}{t}} \]

      5. distribute-lft-out-- 73.2%

         \[\leadsto y + \frac{\color{blue}{-1 \cdot \left(z \cdot \left(y - x\right) - a \cdot \left(y - x\right)\right)}}{t} \]

      6. associate-*r/ 73.2%

         \[\leadsto y + \color{blue}{-1 \cdot \frac{z \cdot \left(y - x\right) - a \cdot \left(y - x\right)}{t}} \]

      7. mul-1-neg 73.2%

         \[\leadsto y + \color{blue}{\left(-\frac{z \cdot \left(y - x\right) - a \cdot \left(y - x\right)}{t}\right)} \]

      8. unsub-neg 73.2%

         \[\leadsto \color{blue}{y - \frac{z \cdot \left(y - x\right) - a \cdot \left(y - x\right)}{t}} \]

      9. distribute-rgt-out-- 73.2%

         \[\leadsto y - \frac{\color{blue}{\left(y - x\right) \cdot \left(z - a\right)}}{t} \]

      10. associate-/l* 82.5%

          \[\leadsto y - \color{blue}{\frac{y - x}{\frac{t}{z - a}}} \]

   7. Simplified 82.5%

      \[\leadsto \color{blue}{y - \frac{y - x}{\frac{t}{z - a}}} \]
3. Recombined 2 regimes into one program.

4. Final simplification 84.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -4.8 \cdot 10^{+95} \lor \neg \left(a \leq 2.6 \cdot 10^{+43}\right):\\ \;\;\;\;x - \frac{x - y}{\frac{a}{z - t}}\\ \mathbf{else}:\\ \;\;\;\;y + \frac{x - y}{\frac{t}{z - a}}\\ \end{array} \]
5. Add Preprocessing

Alternative 23: 37.7% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;a \leq -9 \cdot 10^{+92}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq 1.22 \cdot 10^{+85}:\\ \;\;\;\;y\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= a -9e+92) x (if (<= a 1.22e+85) y x)))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -9e+92) {
		tmp = x;
	} else if (a <= 1.22e+85) {
		tmp = y;
	} else {
		tmp = x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (a <= (-9d+92)) then
        tmp = x
    else if (a <= 1.22d+85) then
        tmp = y
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (a <= -9e+92) {
		tmp = x;
	} else if (a <= 1.22e+85) {
		tmp = y;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if a <= -9e+92:
		tmp = x
	elif a <= 1.22e+85:
		tmp = y
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (a <= -9e+92)
		tmp = x;
	elseif (a <= 1.22e+85)
		tmp = y;
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (a <= -9e+92)
		tmp = x;
	elseif (a <= 1.22e+85)
		tmp = y;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[a, -9e+92], x, If[LessEqual[a, 1.22e+85], y, x]]

Derivation

1. Split input into 2 regimes

2. if a < -8.9999999999999998e92 or 1.22e85 < a

   1. Initial program 70.4%

      \[x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \]
   2. Step-by-step derivation

      1. associate-*l/ 89.0%

         \[\leadsto x + \color{blue}{\frac{y - x}{a - t} \cdot \left(z - t\right)} \]

   3. Simplified 89.0%

      \[\leadsto \color{blue}{x + \frac{y - x}{a - t} \cdot \left(z - t\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in a around inf 60.0%

      \[\leadsto \color{blue}{x} \]

   if -8.9999999999999998e92 < a < 1.22e85

   1. Initial program 61.1%

      \[x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \]
   2. Step-by-step derivation

      1. associate-*l/ 66.0%

         \[\leadsto x + \color{blue}{\frac{y - x}{a - t} \cdot \left(z - t\right)} \]

   3. Simplified 66.0%

      \[\leadsto \color{blue}{x + \frac{y - x}{a - t} \cdot \left(z - t\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in t around inf 37.1%

      \[\leadsto \color{blue}{y} \]
3. Recombined 2 regimes into one program.

4. Final simplification 45.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;a \leq -9 \cdot 10^{+92}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq 1.22 \cdot 10^{+85}:\\ \;\;\;\;y\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 24: 24.2% accurate, 13.0× speedup

Math

\[\begin{array}{l} \\ x \end{array} \]

FPCore

(FPCore (x y z t a) :precision binary64 x)

C

double code(double x, double y, double z, double t, double a) {
	return x;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    code = x
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	return x;
}

Python

def code(x, y, z, t, a):
	return x

Julia

function code(x, y, z, t, a)
	return x
end

MATLAB

function tmp = code(x, y, z, t, a)
	tmp = x;
end

Wolfram

code[x_, y_, z_, t_, a_] := x

Derivation

1. Initial program 64.5%

   \[x + \frac{\left(y - x\right) \cdot \left(z - t\right)}{a - t} \]
2. Step-by-step derivation

   1. associate-*l/ 74.4%

      \[\leadsto x + \color{blue}{\frac{y - x}{a - t} \cdot \left(z - t\right)} \]

3. Simplified 74.4%

   \[\leadsto \color{blue}{x + \frac{y - x}{a - t} \cdot \left(z - t\right)} \]
4. Add Preprocessing

5. Taylor expanded in a around inf 27.3%

   \[\leadsto \color{blue}{x} \]

6. Final simplification 27.3%

   \[\leadsto x \]
7. Add Preprocessing

Developer target: 86.5% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + \frac{y - x}{1} \cdot \frac{z - t}{a - t}\\ \mathbf{if}\;a < -1.6153062845442575 \cdot 10^{-142}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a < 3.774403170083174 \cdot 10^{-182}:\\ \;\;\;\;y - \frac{z}{t} \cdot \left(y - x\right)\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ x (* (/ (- y x) 1.0) (/ (- z t) (- a t))))))
   (if (< a -1.6153062845442575e-142)
     t_1
     (if (< a 3.774403170083174e-182) (- y (* (/ z t) (- y x))) t_1))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x + (((y - x) / 1.0) * ((z - t) / (a - t)));
	double tmp;
	if (a < -1.6153062845442575e-142) {
		tmp = t_1;
	} else if (a < 3.774403170083174e-182) {
		tmp = y - ((z / t) * (y - x));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x + (((y - x) / 1.0d0) * ((z - t) / (a - t)))
    if (a < (-1.6153062845442575d-142)) then
        tmp = t_1
    else if (a < 3.774403170083174d-182) then
        tmp = y - ((z / t) * (y - x))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = x + (((y - x) / 1.0) * ((z - t) / (a - t)));
	double tmp;
	if (a < -1.6153062845442575e-142) {
		tmp = t_1;
	} else if (a < 3.774403170083174e-182) {
		tmp = y - ((z / t) * (y - x));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x + (((y - x) / 1.0) * ((z - t) / (a - t)))
	tmp = 0
	if a < -1.6153062845442575e-142:
		tmp = t_1
	elif a < 3.774403170083174e-182:
		tmp = y - ((z / t) * (y - x))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x + Float64(Float64(Float64(y - x) / 1.0) * Float64(Float64(z - t) / Float64(a - t))))
	tmp = 0.0
	if (a < -1.6153062845442575e-142)
		tmp = t_1;
	elseif (a < 3.774403170083174e-182)
		tmp = Float64(y - Float64(Float64(z / t) * Float64(y - x)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x + (((y - x) / 1.0) * ((z - t) / (a - t)));
	tmp = 0.0;
	if (a < -1.6153062845442575e-142)
		tmp = t_1;
	elseif (a < 3.774403170083174e-182)
		tmp = y - ((z / t) * (y - x));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x + N[(N[(N[(y - x), $MachinePrecision] / 1.0), $MachinePrecision] * N[(N[(z - t), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[Less[a, -1.6153062845442575e-142], t$95$1, If[Less[a, 3.774403170083174e-182], N[(y - N[(N[(z / t), $MachinePrecision] * N[(y - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]

Reproduce

herbie shell --seed 2024021 
(FPCore (x y z t a)
  :name "Graphics.Rendering.Chart.Axis.Types:linMap from Chart-1.5.3"
  :precision binary64

  :herbie-target
  (if (< a -1.6153062845442575e-142) (+ x (* (/ (- y x) 1.0) (/ (- z t) (- a t)))) (if (< a 3.774403170083174e-182) (- y (* (/ z t) (- y x))) (+ x (* (/ (- y x) 1.0) (/ (- z t) (- a t))))))

  (+ x (/ (* (- y x) (- z t)) (- a t))))